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Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 192 (from laksa088)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa192.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.splashlearn.com/math-vocabulary/binary-multiplication\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.splashlearn.com/math-vocabulary/binary-multiplication\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication","crawl_time":1775924010,"first_indexed_time":1699500881,"http_code":200,"src_unparsed":"com,splashlearn!www,\/math-vocabulary\/binary-multiplication s443","src_root_hash":"9809215980688736792","history_drop_reason":null,"meta_title":"Binary Multiplication - Rules, Types, Steps, Examples","meta_descriptions":["Binary multiplication is a fundamental operation on binary numbers which is carried out using binary multiplication rules. Learn the steps, examples, and more."],"attrs_boilerpipe_text":"Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The\nmultiplication\nof binary numbers can be calculated using the binary multiplication rules.\n \nWhat is the Binary Number System?\nA binary number system is the base-2\nnumber system\n. It uses only two digits, 0 and 1 to form all the numbers. Each\ndigit\nin the binary number system is said to be a bit.\nIf you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules.\nRules of Binary Multiplication\nJust like decimal multiplication, we define a\nmultiplier\nand a multiplicand in the binary multiplication. The result of multiplication is called a product. \nBinary Multiplication Rules:\n0 × 0 = 0\n0 × 1 = 0\n1 × 0 = 0\n1 × 1 = 1  \nBinary Multiplication Table\nWe can create a binary multiplication table using the rules mentioned above like this:\n×\n0\n1\n0\n0\n0\n1\n0\n1\nWe can also summarize the rules in the binary multiplication table as:\nMultiplicand\nMultiplier\nProduct\n0\n0\n0 × 0 = 0\n0\n1\n0 × 1 = 0\n1\n0\n1 × 0 = 0\n1\n1\n1 × 1 = 1\nNote: \nWhen we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful.\nBinary Addition Rules:\n0 + 0 = 0\n0 + 1 = 1\n1 + 0 = 1\n1 + 1 = 0 (carry 1)\nHow to Perform Binary Multiplication\nLet’s understand the binary multiplication with steps. Consider the following example.\nBinary multiplication example:\nMultiply 1010\n2\nand 1011\n2\n. \nThe rules for binary multiplication are as follows: \nStep 1:\nWrite down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method.\nStep 2:\nMultiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number).\nHere, we will multiply all the digits of (1010)\n2\nwith the rightmost digit of 1011\n2\n, which is 1. We call the result as the partial product.\nStep 3:\nIn the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place).\nStep 3:\nRepeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand.\nStep 5:\nFinally, add all the partial products. To add all the binary numbers use the rules of binary addition.\nExample 2:\nFind the product of\n1001\n2\nand 101\n2\n.\nFacts about Binary Multiplication\nYou can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system.\nConclusion\nIn this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems.  \nSolved Examples on Binary Multiplication\n1. Multiply (101)\n2\nby (11)\n2\n.\nVerify your answer.\nSolution:\n (101)\n2\n× (11)\n2\n= (01111)\n2\n(101)\n2\n= 5\n10\n(11)2 = 3\n10\nProduct = 5 × 3 = 15\n15\n10\n=  1111\n2\n2. Find the product of (110)\n2\nby (100)\n2\n. \nSolution: \nLet’s multiply (110)\n2\nby (100)\n2\n.\n(110)\n2\n×\n(100)\n2\n= (11000)\n2\nDecimal value: 6 × 4 = 24\n3. What is the product of (1101)\n2\nby (111)\n2\n?\nSolution: \nLet’s multiply\n(1101)\n2\nby\n(111)\n2\n.\n(1101)\n2\n×\n(111)\n2\n=\n(01011011)\n2\nDecimal value: 13 × 7 = 91\nPractice Problems on Binary Multiplication\n- 1\n2\n1\n0\nCorrect answer is: 0\n0 × 0 = 0\n10\n1\n0\n20\nCorrect answer is: 1\n1 × 1 = 1\n$1_{2}$\n$111_{2}$\n$1110_{2}$\n$1011_{2}$\nCorrect answer is: $1110_{2}$\n$111_{2} \\times 10_{2} = 1110_{2}$\n$(1111)_{2}$\n$(0111011)_{2}$\n$(1111111)_{2}$\n$(0111111)_{2}$\nCorrect answer is: $(0111111)_{2}$\n$(1001)_{2} \\times (111)_{2} = (0111111)_{2}$\nFrequently Asked Questions on Binary Multiplication\nWhat is the 1’s complement of a binary number?\nThe 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1.\n1’s complement of 111 is 000. \n1’s complement of 10101 is 010101.\nHow does binary multiplication work?\nBinary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result.\nWhat are binary multiplication rules?\n0 × 0 = 0\n0 × 1 = 0\n1 × 0 = 0\n1 × 1 = 1","attrs_markdown":"[![SplashLearn Logo](https:\/\/cdn.splashmath.com\/assets\/home\/v5\/logo-a26c535e83d56f82115a35713fd8c41179a928c83b9cef3bac76e9dc28c27c02.png)](https:\/\/www.splashlearn.com\/)\n\n[Parents ![Chevron down](https:\/\/cdn.splashmath.com\/assets\/home\/v5\/chevron-down-b79420fa977804bd61f4bf84f2e0fe100008b5b82b29b6d25493b63b6d6329de.svg)]()\n\n![graduation-cap-icon](https:\/\/cdn.splashmath.com\/assets\/home\/v5\/graduation-cap-icon-3b600937e7d971b772c266139b40d06d1a1a2658bcdcd045b320cc673801bb73.svg)\n\nExplore by Grade\n\n[Preschool (Age 2-5)](https:\/\/www.splashlearn.com\/preschoolers)[Kindergarten](https:\/\/www.splashlearn.com\/kindergarteners)[Grade 1](https:\/\/www.splashlearn.com\/1st-graders)[Grade 2](https:\/\/www.splashlearn.com\/2nd-graders)[Grade 3](https:\/\/www.splashlearn.com\/3rd-graders)[Grade 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Table](https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#2-binary-multiplication-table)\n- [Solved Examples on Binary Multiplication](https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#6-solved-examples-on-binary-multiplication)\n- [Practice Problems on Binary Multiplication](https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#7-practice-problems-on-binary-multiplication)\n- [Frequently Asked Questions on Binary Multiplication](https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#8-frequently-asked-questions-on-binary-multiplication)\n## What Is Binary Multiplication?\n**Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The** [**multiplication**](https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication) **of binary numbers can be calculated using the binary multiplication rules.**\n\n**What is the Binary Number System?**\n\nA binary number system is the base-2 [number system](https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-system). It uses only two digits, 0 and 1 to form all the numbers. Each [digit](https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/digit) in the binary number system is said to be a bit.\n\nIf you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules.\n\n#### Recommended Games\n[![Choose the Correct Product for the Multiplication Expressions Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_match_4dby1d_fluently_pt.png) Choose the Correct Product for the Multiplication Expressions Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-product-for-the-multiplication-expressions)\n\n[![Choose the Missing Number in the Multiplication Solution Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_missing_2dby1d_pt.png) Choose the Missing Number in the Multiplication Solution Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-missing-number-in-the-multiplication-solution)\n\n[![Choose the Multiplication Expression Representing Fraction Models Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_mult_unit_by_whole_pt.png) Choose the Multiplication Expression Representing Fraction Models Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-multiplication-expression-representing-fraction-models)\n\n[![Choose the Product for the Multiplication Questions Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_product_4dby1d_1_pt.png) Choose the Product for the Multiplication Questions Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-product-for-the-multiplication-questions)\n\n[![Choose to Complete each of the Multiplication Expressions Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_match_3dby1d_fluently_pt.png) Choose to Complete each of the Multiplication Expressions Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/choose-to-complete-each-of-the-multiplication-expressions)\n\n[![Complete the Decimal Multiplication Pattern Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_complete_mul_pattern_pt.png) Complete the Decimal Multiplication Pattern Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-decimal-multiplication-pattern)\n\n[![Complete the Multiplication Between Fractions and Whole Numbers Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_complete_multiplication_pt.png) Complete the Multiplication Between Fractions and Whole Numbers Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-between-fractions-and-whole-numbers)\n\n[![Complete the Multiplication Expression Using the Fraction Models Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_multiply_models_unit_by_whole_pt.png) Complete the Multiplication Expression Using the Fraction Models Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-expression-using-the-fraction-models)\n\n[![Complete the Multiplication Fact of 11 Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_missing_num_pt.png) Complete the Multiplication Fact of 11 Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-fact-of-11)\n\n[![Complete the Multiplication Facts of 2 Game](https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_numMissing2_pt.png) Complete the Multiplication Facts of 2 Game Play](https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-facts-of-2)\n\n[More Games](https:\/\/www.splashlearn.com\/games)\n## Rules of Binary Multiplication\nJust like decimal multiplication, we define a [multiplier](https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplier) and a multiplicand in the binary multiplication. The result of multiplication is called a product.\n\nBinary Multiplication Rules:\n\n- 0 × 0 = 0\n- 0 × 1 = 0\n- 1 × 0 = 0\n- 1 × 1 = 1\n\n#### Recommended Worksheets\n[![Addition and Multiplication Expression for Array Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expression-for-array.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expression-for-array)\n\n[![Addition and Multiplication Expressions Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expressions.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expressions)\n\n[![Apply Multiplication in Everyday Life Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-multiplication-in-everyday-life.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-multiplication-in-everyday-life)\n\n[![Break the Multiplication Expression Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-the-multiplication-expression.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-the-multiplication-expression)\n\n[![Choose Your own Multiplication Strategy Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/choose-your-own-multiplication-strategy.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/choose-your-own-multiplication-strategy)\n\n[![Commutative Property of Multiplication Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-multiplication.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-multiplication)\n\n[![Compare the Multiplication Expressions Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-the-multiplication-expressions.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-the-multiplication-expressions)\n\n[![Comparing Multiplication Expressions Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/comparing-multiplication-expressions.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/comparing-multiplication-expressions)\n\n[![Complete Multiplication and Division Sentences Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-multiplication-and-division-sentences.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-multiplication-and-division-sentences)\n\n[![Complete Multiplication Sentence Worksheet](https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-multiplication-sentence.jpeg)](https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-multiplication-sentence)\n\n[More Worksheets](https:\/\/www.splashlearn.com\/worksheets)\n## Binary Multiplication Table\nWe can create a binary multiplication table using the rules mentioned above like this:\n\n|   |   |   |\n|---|---|---|\n| × | 0 | 1 |\n| 0 | 0 | 0 |\n| 1 | 0 | 1 |\n\nWe can also summarize the rules in the binary multiplication table as:\n\n| **Multiplicand** | **Multiplier** | **Product** |\n|---|---|---|\n| 0 | 0 | 0 × 0 = 0 |\n| 0 | 1 | 0 × 1 = 0 |\n| 1 | 0 | 1 × 0 = 0 |\n| 1 | 1 | 1 × 1 = 1 |\n\n**Note:**\n\nWhen we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful.\n\n**Binary Addition Rules:**\n\n- 0 + 0 = 0\n- 0 + 1 = 1\n- 1 + 0 = 1\n- 1 + 1 = 0 (carry 1)\n## How to Perform Binary Multiplication\nLet’s understand the binary multiplication with steps. Consider the following example.\n\n**Binary multiplication example:** Multiply 10102 and 10112.\n\nThe rules for binary multiplication are as follows:\n\n**Step 1:** Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method.\n\n![Binary multiplication step 1](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-1.png)\n\n**Step 2:** Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number).\n\nHere, we will multiply all the digits of (1010)2 with the rightmost digit of 10112, which is 1. We call the result as the partial product.\n\n![Binary multiplication step 2](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-2.png)\n\n**Step 3:** In the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place).\n\n![Binary multiplication step 3](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-3.png)\n\n**Step 3:** Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand.\n\n![Binary multiplication step 4](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-4.png)\n\n**Step 5:** Finally, add all the partial products. To add all the binary numbers use the rules of binary addition.\n\n![Binary Multiplication \\&\\#8211; Rules, Types, Steps, Examples, FAQs](https:\/\/lh7-us.googleusercontent.com\/gPzQAD3zZM7rjrLWPsh1uje5rh29awwdqr25BAs8ELWQpJZjGCne2g7w5MEQxtwJnKY_pqj1tYKRQ2Sy4uTLJ11F6nml-ss3LgePmFUdfhXiPcKGgX-WSlD2lEKvCq53WEpp0zU8ynIGmg5QtfM3m7s)\n\n**Example 2:** Find the product of10012 and 1012.\n\n![Binary multiplication of 1001 and 101](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1001-and-101.png)\n\n## Facts about Binary Multiplication\n- You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system.\n## Conclusion\nIn this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems.\n\n## Solved Examples on Binary Multiplication\n**1\\. Multiply (101)2 by (11)2.**\n\n**Verify your answer.**\n\n**Solution:**\n\n(101)2 × (11)2 = (01111)2\n\n![Binary multiplication of 101 and 11](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-101-and-11.png)\n\n**(101)****2**\\= 510\n\n(11)2 = 310\n\nProduct = 5 × 3 = 15\n\n1510 = 11112\n\n**2\\. Find the product of (110)2 by (100)2.**\n\n**Solution:**\n\nLet’s multiply (110)2 by (100)2.\n\n![Binary multiplication of 110 and 100](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-110-and-100.png)\n\n**(110)2** × **(100)2** = (11000)2\n\nDecimal value: 6 × 4 = 24\n\n**3\\. What is the product of (1101)2 by (111)2?**\n\n**Solution:**\n\nLet’s multiply **(1101)2** by **(111)2.**\n\n![Binary multiplication of 1101 and 111](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1101-and-111.png)\n\n**(1101)2** × **(111)2** = **(01011011)2**\n\nDecimal value: 13 × 7 = 91\n\n## Practice Problems on Binary Multiplication\n## Binary Multiplication - Rules, Types, Steps, Examples, FAQs\nAttend this quiz & Test your knowledge.\n\n1\n\n### In the binary decimal number system, the product of 0 and 0 is \\_\\_\\_\\_.\n\n\\- 1\n\n2\n\n1\n\n0\n\nCorrectIncorrect\n\nCorrect answer is: 0  \n0 × 0 = 0\n\n2\n\n### What is the product of 1 and 1 in binary multiplication?\n\n10\n\n1\n\n0\n\n20\n\nCorrectIncorrect\n\nCorrect answer is: 1  \n1 × 1 = 1\n\n3\n\n### Using binary multiplication rules, find \\$(111)\\_{2}\\$ by \\$(10)\\_{2}\\$.\n\n\\$1\\_{2}\\$\n\n\\$111\\_{2}\\$\n\n\\$1110\\_{2}\\$\n\n\\$1011\\_{2}\\$\n\nCorrectIncorrect\n\nCorrect answer is: \\$1110\\_{2}\\$  \n\\$111\\_{2} \\\\times 10\\_{2} = 1110\\_{2}\\$\n\n4\n\n### The product of \\$(1001)\\_{2}\\$ by \\$(111)\\_{2}\\$ is \\_\\_\\_\\_.\n\n\\$(1111)\\_{2}\\$\n\n\\$(0111011)\\_{2}\\$\n\n\\$(1111111)\\_{2}\\$\n\n\\$(0111111)\\_{2}\\$\n\nCorrectIncorrect\n\nCorrect answer is: \\$(0111111)\\_{2}\\$  \n\\$(1001)\\_{2} \\\\times (111)\\_{2} = (0111111)\\_{2}\\$\n## Frequently Asked Questions on Binary Multiplication\n**What is the 1’s complement of a binary number?**\n\nThe 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1.  \n1’s complement of 111 is 000.   \n1’s complement of 10101 is 010101.\n\n**How does binary multiplication work?**\n\nBinary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result.\n\n**What are binary multiplication rules?**\n\n- 0 × 0 = 0\n- 0 × 1 = 0\n- 1 × 0 = 0\n- 1 × 1 = 1\n\n##### RELATED POSTS\n- [Factor Tree – Definition with Examples](https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree \"Factor Tree – Definition with Examples\")\n- [Converting Fractions into Decimals – Methods, Facts, Examples](https:\/\/www.splashlearn.com\/math-vocabulary\/convert-fraction-to-decimal \"Converting Fractions into Decimals – Methods, Facts, Examples\")\n- [Math Symbols – Definition with Examples](https:\/\/www.splashlearn.com\/math-vocabulary\/math-symbols \"Math Symbols – Definition with Examples\")\n- [270 Degree Angle – Construction, in Radians, Examples, FAQs](https:\/\/www.splashlearn.com\/math-vocabulary\/270-degree-angle \"270 Degree Angle – Construction, in Radians, Examples, FAQs\")\n- [Math Glossary Terms beginning with Z](https:\/\/www.splashlearn.com\/math-vocabulary\/letter-z \"Math Glossary Terms beginning 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The** [**multiplication**](https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication) **of binary numbers can be calculated using the binary multiplication rules.**\n\n**What is the Binary Number System?**\n\nA binary number system is the base-2 [number system](https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-system). It uses only two digits, 0 and 1 to form all the numbers. Each [digit](https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/digit) in the binary number system is said to be a bit.\n\nIf you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules.\n\n## Rules of Binary Multiplication\nJust like decimal multiplication, we define a [multiplier](https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplier) and a multiplicand in the binary multiplication. The result of multiplication is called a product.\n\nBinary Multiplication Rules:\n\n- 0 × 0 = 0\n- 0 × 1 = 0\n- 1 × 0 = 0\n- 1 × 1 = 1\n## Binary Multiplication Table\nWe can create a binary multiplication table using the rules mentioned above like this:\n\n|   |   |   |\n|---|---|---|\n| × | 0 | 1 |\n| 0 | 0 | 0 |\n| 1 | 0 | 1 |\n\nWe can also summarize the rules in the binary multiplication table as:\n\n| **Multiplicand** | **Multiplier** | **Product** |\n|---|---|---|\n| 0 | 0 | 0 × 0 = 0 |\n| 0 | 1 | 0 × 1 = 0 |\n| 1 | 0 | 1 × 0 = 0 |\n| 1 | 1 | 1 × 1 = 1 |\n\n**Note:**\n\nWhen we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful.\n\n**Binary Addition Rules:**\n\n- 0 + 0 = 0\n- 0 + 1 = 1\n- 1 + 0 = 1\n- 1 + 1 = 0 (carry 1)\n## How to Perform Binary Multiplication\nLet’s understand the binary multiplication with steps. Consider the following example.\n\n**Binary multiplication example:** Multiply 10102 and 10112.\n\nThe rules for binary multiplication are as follows:\n\n**Step 1:** Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method.\n\n![Binary multiplication step 1](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-1.png)\n\n**Step 2:** Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number).\n\nHere, we will multiply all the digits of (1010)2 with the rightmost digit of 10112, which is 1. We call the result as the partial product.\n\n![Binary multiplication step 2](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-2.png)\n\n**Step 3:** In the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place).\n\n![Binary multiplication step 3](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-3.png)\n\n**Step 3:** Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand.\n\n![Binary multiplication step 4](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-4.png)\n\n**Step 5:** Finally, add all the partial products. To add all the binary numbers use the rules of binary addition.\n\n![Binary Multiplication \\&\\#8211; Rules, Types, Steps, Examples, FAQs](https:\/\/lh7-us.googleusercontent.com\/gPzQAD3zZM7rjrLWPsh1uje5rh29awwdqr25BAs8ELWQpJZjGCne2g7w5MEQxtwJnKY_pqj1tYKRQ2Sy4uTLJ11F6nml-ss3LgePmFUdfhXiPcKGgX-WSlD2lEKvCq53WEpp0zU8ynIGmg5QtfM3m7s)\n\n**Example 2:** Find the product of10012 and 1012.\n\n![Binary multiplication of 1001 and 101](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1001-and-101.png)\n\n## Facts about Binary Multiplication\n- You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system.\n## Conclusion\nIn this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems.\n\n## Solved Examples on Binary Multiplication\n**1\\. Multiply (101)2 by (11)2.**\n\n**Verify your answer.**\n\n**Solution:**\n\n(101)2 × (11)2 = (01111)2\n\n![Binary multiplication of 101 and 11](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-101-and-11.png)\n\n**(101)****2**\\= 510\n\n(11)2 = 310\n\nProduct = 5 × 3 = 15\n\n1510 = 11112\n\n**2\\. Find the product of (110)2 by (100)2.**\n\n**Solution:**\n\nLet’s multiply (110)2 by (100)2.\n\n![Binary multiplication of 110 and 100](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-110-and-100.png)\n\n**(110)2** × **(100)2** = (11000)2\n\nDecimal value: 6 × 4 = 24\n\n**3\\. What is the product of (1101)2 by (111)2?**\n\n**Solution:**\n\nLet’s multiply **(1101)2** by **(111)2.**\n\n![Binary multiplication of 1101 and 111](https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1101-and-111.png)\n\n**(1101)2** × **(111)2** = **(01011011)2**\n\nDecimal value: 13 × 7 = 91\n\n## Practice Problems on Binary Multiplication\n\\- 1\n\n2\n\n1\n\n0\n\nCorrect answer is: 0  \n0 × 0 = 0\n\n10\n\n1\n\n0\n\n20\n\nCorrect answer is: 1  \n1 × 1 = 1\n\n\\$1\\_{2}\\$\n\n\\$111\\_{2}\\$\n\n\\$1110\\_{2}\\$\n\n\\$1011\\_{2}\\$\n\nCorrect answer is: \\$1110\\_{2}\\$  \n\\$111\\_{2} \\\\times 10\\_{2} = 1110\\_{2}\\$\n\n\\$(1111)\\_{2}\\$\n\n\\$(0111011)\\_{2}\\$\n\n\\$(1111111)\\_{2}\\$\n\n\\$(0111111)\\_{2}\\$\n\nCorrect answer is: \\$(0111111)\\_{2}\\$  \n\\$(1001)\\_{2} \\\\times (111)\\_{2} = (0111111)\\_{2}\\$\n## Frequently Asked Questions on Binary Multiplication\n**What is the 1’s complement of a binary number?**\n\nThe 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1.  \n1’s complement of 111 is 000.   \n1’s complement of 10101 is 010101.\n\n**How does binary multiplication work?**\n\nBinary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result.\n\n**What are binary multiplication rules?**\n\n- 0 × 0 = 0\n- 0 × 1 = 0\n- 1 × 0 = 0\n- 1 × 1 = 1","meta_canonical":null}

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Boilerpipe Text	Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The multiplication of binary numbers can be calculated using the binary multiplication rules. What is the Binary Number System? A binary number system is the base-2 number system . It uses only two digits, 0 and 1 to form all the numbers. Each digit in the binary number system is said to be a bit. If you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules. Rules of Binary Multiplication Just like decimal multiplication, we define a multiplier and a multiplicand in the binary multiplication. The result of multiplication is called a product. Binary Multiplication Rules: 0 × 0 = 0 0 × 1 = 0 1 × 0 = 0 1 × 1 = 1 Binary Multiplication Table We can create a binary multiplication table using the rules mentioned above like this: × 0 1 0 0 0 1 0 1 We can also summarize the rules in the binary multiplication table as: Multiplicand Multiplier Product 0 0 0 × 0 = 0 0 1 0 × 1 = 0 1 0 1 × 0 = 0 1 1 1 × 1 = 1 Note: When we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful. Binary Addition Rules: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 (carry 1) How to Perform Binary Multiplication Let’s understand the binary multiplication with steps. Consider the following example. Binary multiplication example: Multiply 1010 2 and 1011 2 . The rules for binary multiplication are as follows: Step 1: Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method. Step 2: Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number). Here, we will multiply all the digits of (1010) 2 with the rightmost digit of 1011 2 , which is 1. We call the result as the partial product. Step 3: In the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place). Step 3: Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand. Step 5: Finally, add all the partial products. To add all the binary numbers use the rules of binary addition. Example 2: Find the product of 1001 2 and 101 2 . Facts about Binary Multiplication You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system. Conclusion In this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems. Solved Examples on Binary Multiplication 1. Multiply (101) 2 by (11) 2 . Verify your answer. Solution: (101) 2 × (11) 2 = (01111) 2 (101) 2 = 5 10 (11)2 = 3 10 Product = 5 × 3 = 15 15 10 = 1111 2 2. Find the product of (110) 2 by (100) 2 . Solution: Let’s multiply (110) 2 by (100) 2 . (110) 2 × (100) 2 = (11000) 2 Decimal value: 6 × 4 = 24 3. What is the product of (1101) 2 by (111) 2 ? Solution: Let’s multiply (1101) 2 by (111) 2 . (1101) 2 × (111) 2 = (01011011) 2 Decimal value: 13 × 7 = 91 Practice Problems on Binary Multiplication - 1 2 1 0 Correct answer is: 0 0 × 0 = 0 10 1 0 20 Correct answer is: 1 1 × 1 = 1 $1_{2}$ $111_{2}$ $1110_{2}$ $1011_{2}$ Correct answer is: $1110_{2}$ $111_{2} \times 10_{2} = 1110_{2}$ $(1111)_{2}$ $(0111011)_{2}$ $(1111111)_{2}$ $(0111111)_{2}$ Correct answer is: $(0111111)_{2}$ $(1001)_{2} \times (111)_{2} = (0111111)_{2}$ Frequently Asked Questions on Binary Multiplication What is the 1’s complement of a binary number? The 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1. 1’s complement of 111 is 000. 1’s complement of 10101 is 010101. How does binary multiplication work? Binary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result. What are binary multiplication rules? 0 × 0 = 0 0 × 1 = 0 1 × 0 = 0 1 × 1 = 1
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Table](https://www.splashlearn.com/math-vocabulary/binary-multiplication#2-binary-multiplication-table) - [Solved Examples on Binary Multiplication](https://www.splashlearn.com/math-vocabulary/binary-multiplication#6-solved-examples-on-binary-multiplication) - [Practice Problems on Binary Multiplication](https://www.splashlearn.com/math-vocabulary/binary-multiplication#7-practice-problems-on-binary-multiplication) - [Frequently Asked Questions on Binary Multiplication](https://www.splashlearn.com/math-vocabulary/binary-multiplication#8-frequently-asked-questions-on-binary-multiplication) ## What Is Binary Multiplication? Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The [multiplication](https://www.splashlearn.com/math-vocabulary/multiplication/multiplication) of binary numbers can be calculated using the binary multiplication rules. What is the Binary Number System? A binary number system is the base-2 [number system](https://www.splashlearn.com/math-vocabulary/number-sense/number-system). It uses only two digits, 0 and 1 to form all the numbers. Each [digit](https://www.splashlearn.com/math-vocabulary/number-sense/digit) in the binary number system is said to be a bit. If you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules. #### Recommended Games [![Choose the Correct Product for the Multiplication Expressions Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_pv_mult_match_4dby1d_fluently_pt.png) Choose the Correct Product for the Multiplication Expressions Game Play](https://www.splashlearn.com/s/math-games/choose-the-correct-product-for-the-multiplication-expressions) [![Choose the Missing Number in the Multiplication Solution Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_pv_find_missing_2dby1d_pt.png) Choose the Missing Number in the Multiplication Solution Game Play](https://www.splashlearn.com/s/math-games/choose-the-missing-number-in-the-multiplication-solution) [![Choose the Multiplication Expression Representing Fraction Models Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/fractions_represent_mult_unit_by_whole_pt.png) Choose the Multiplication Expression Representing Fraction Models Game Play](https://www.splashlearn.com/s/math-games/choose-the-multiplication-expression-representing-fraction-models) [![Choose the Product for the Multiplication Questions Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_pv_find_product_4dby1d_1_pt.png) Choose the Product for the Multiplication Questions Game Play](https://www.splashlearn.com/s/math-games/choose-the-product-for-the-multiplication-questions) [![Choose to Complete each of the Multiplication Expressions Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_pv_mult_match_3dby1d_fluently_pt.png) Choose to Complete each of the Multiplication Expressions Game Play](https://www.splashlearn.com/s/math-games/choose-to-complete-each-of-the-multiplication-expressions) [![Complete the Decimal Multiplication Pattern Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/dec_mul_div_complete_mul_pattern_pt.png) Complete the Decimal Multiplication Pattern Game Play](https://www.splashlearn.com/s/math-games/complete-the-decimal-multiplication-pattern) [![Complete the Multiplication Between Fractions and Whole Numbers Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/fractions_complete_multiplication_pt.png) Complete the Multiplication Between Fractions and Whole Numbers Game Play](https://www.splashlearn.com/s/math-games/complete-the-multiplication-between-fractions-and-whole-numbers) [![Complete the Multiplication Expression Using the Fraction Models Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/fractions_multiply_models_unit_by_whole_pt.png) Complete the Multiplication Expression Using the Fraction Models Game Play](https://www.splashlearn.com/s/math-games/complete-the-multiplication-expression-using-the-fraction-models) [![Complete the Multiplication Fact of 11 Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_pv_missing_num_pt.png) Complete the Multiplication Fact of 11 Game Play](https://www.splashlearn.com/s/math-games/complete-the-multiplication-fact-of-11) [![Complete the Multiplication Facts of 2 Game](https://cdn.splashmath.com/curriculum_uploads/images/playables/mult_div_facts_mul_numMissing2_pt.png) Complete the Multiplication Facts of 2 Game Play](https://www.splashlearn.com/s/math-games/complete-the-multiplication-facts-of-2) [More Games](https://www.splashlearn.com/games) ## Rules of Binary Multiplication Just like decimal multiplication, we define a [multiplier](https://www.splashlearn.com/math-vocabulary/multiplication/multiplier) and a multiplicand in the binary multiplication. The result of multiplication is called a product. Binary Multiplication Rules: - 0 × 0 = 0 - 0 × 1 = 0 - 1 × 0 = 0 - 1 × 1 = 1 #### Recommended Worksheets [![Addition and Multiplication Expression for Array Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/addition-and-multiplication-expression-for-array.jpeg)](https://www.splashlearn.com/s/math-worksheets/addition-and-multiplication-expression-for-array) [![Addition and Multiplication Expressions Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/addition-and-multiplication-expressions.jpeg)](https://www.splashlearn.com/s/math-worksheets/addition-and-multiplication-expressions) [![Apply Multiplication in Everyday Life Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/apply-multiplication-in-everyday-life.jpeg)](https://www.splashlearn.com/s/math-worksheets/apply-multiplication-in-everyday-life) [![Break the Multiplication Expression Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/break-the-multiplication-expression.jpeg)](https://www.splashlearn.com/s/math-worksheets/break-the-multiplication-expression) [![Choose Your own Multiplication Strategy Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/choose-your-own-multiplication-strategy.jpeg)](https://www.splashlearn.com/s/math-worksheets/choose-your-own-multiplication-strategy) [![Commutative Property of Multiplication Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/commutative-property-of-multiplication.jpeg)](https://www.splashlearn.com/s/math-worksheets/commutative-property-of-multiplication) [![Compare the Multiplication Expressions Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/compare-the-multiplication-expressions.jpeg)](https://www.splashlearn.com/s/math-worksheets/compare-the-multiplication-expressions) [![Comparing Multiplication Expressions Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/comparing-multiplication-expressions.jpeg)](https://www.splashlearn.com/s/math-worksheets/comparing-multiplication-expressions) [![Complete Multiplication and Division Sentences Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/complete-multiplication-and-division-sentences.jpeg)](https://www.splashlearn.com/s/math-worksheets/complete-multiplication-and-division-sentences) [![Complete Multiplication Sentence Worksheet](https://cdn.splashmath.com/cms_assets/s/math-worksheets/complete-multiplication-sentence.jpeg)](https://www.splashlearn.com/s/math-worksheets/complete-multiplication-sentence) [More Worksheets](https://www.splashlearn.com/worksheets) ## Binary Multiplication Table We can create a binary multiplication table using the rules mentioned above like this: \| \| \| \| \|---\|---\|---\| \| × \| 0 \| 1 \| \| 0 \| 0 \| 0 \| \| 1 \| 0 \| 1 \| We can also summarize the rules in the binary multiplication table as: \| Multiplicand \| Multiplier \| Product \| \|---\|---\|---\| \| 0 \| 0 \| 0 × 0 = 0 \| \| 0 \| 1 \| 0 × 1 = 0 \| \| 1 \| 0 \| 1 × 0 = 0 \| \| 1 \| 1 \| 1 × 1 = 1 \| Note: When we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful. Binary Addition Rules: - 0 + 0 = 0 - 0 + 1 = 1 - 1 + 0 = 1 - 1 + 1 = 0 (carry 1) ## How to Perform Binary Multiplication Let’s understand the binary multiplication with steps. Consider the following example. Binary multiplication example: Multiply 10102 and 10112. The rules for binary multiplication are as follows: Step 1: Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method. ![Binary multiplication step 1](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-1.png) Step 2: Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number). Here, we will multiply all the digits of (1010)2 with the rightmost digit of 10112, which is 1. We call the result as the partial product. ![Binary multiplication step 2](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-2.png) Step 3: In the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place). ![Binary multiplication step 3](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-3.png) Step 3: Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand. ![Binary multiplication step 4](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-4.png) Step 5: Finally, add all the partial products. To add all the binary numbers use the rules of binary addition. ![Binary Multiplication \&\#8211; Rules, Types, Steps, Examples, FAQs](https://lh7-us.googleusercontent.com/gPzQAD3zZM7rjrLWPsh1uje5rh29awwdqr25BAs8ELWQpJZjGCne2g7w5MEQxtwJnKY_pqj1tYKRQ2Sy4uTLJ11F6nml-ss3LgePmFUdfhXiPcKGgX-WSlD2lEKvCq53WEpp0zU8ynIGmg5QtfM3m7s) Example 2: Find the product of10012 and 1012. ![Binary multiplication of 1001 and 101](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-1001-and-101.png) ## Facts about Binary Multiplication - You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system. ## Conclusion In this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems. ## Solved Examples on Binary Multiplication 1\. Multiply (101)2 by (11)2. Verify your answer. Solution: (101)2 × (11)2 = (01111)2 ![Binary multiplication of 101 and 11](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-101-and-11.png) (101)2\= 510 (11)2 = 310 Product = 5 × 3 = 15 1510 = 11112 2\. Find the product of (110)2 by (100)2. Solution: Let’s multiply (110)2 by (100)2. ![Binary multiplication of 110 and 100](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-110-and-100.png) (110)2 × (100)2 = (11000)2 Decimal value: 6 × 4 = 24 3\. What is the product of (1101)2 by (111)2? Solution: Let’s multiply (1101)2 by (111)2. ![Binary multiplication of 1101 and 111](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-1101-and-111.png) (1101)2 × (111)2 = (01011011)2 Decimal value: 13 × 7 = 91 ## Practice Problems on Binary Multiplication ## Binary Multiplication - Rules, Types, Steps, Examples, FAQs Attend this quiz & Test your knowledge. 1 ### In the binary decimal number system, the product of 0 and 0 is \_\_\_\_. \- 1 2 1 0 CorrectIncorrect Correct answer is: 0 0 × 0 = 0 2 ### What is the product of 1 and 1 in binary multiplication? 10 1 0 20 CorrectIncorrect Correct answer is: 1 1 × 1 = 1 3 ### Using binary multiplication rules, find \$(111)\_{2}\$ by \$(10)\_{2}\$. \$1\_{2}\$ \$111\_{2}\$ \$1110\_{2}\$ \$1011\_{2}\$ CorrectIncorrect Correct answer is: \$1110\_{2}\$ \$111\_{2} \\times 10\_{2} = 1110\_{2}\$ 4 ### The product of \$(1001)\_{2}\$ by \$(111)\_{2}\$ is \_\_\_\_. \$(1111)\_{2}\$ \$(0111011)\_{2}\$ \$(1111111)\_{2}\$ \$(0111111)\_{2}\$ CorrectIncorrect Correct answer is: \$(0111111)\_{2}\$ \$(1001)\_{2} \\times (111)\_{2} = (0111111)\_{2}\$ ## Frequently Asked Questions on Binary Multiplication What is the 1’s complement of a binary number? The 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1. 1’s complement of 111 is 000. 1’s complement of 10101 is 010101. How does binary multiplication work? Binary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result. 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Readable Markdown	Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The [multiplication](https://www.splashlearn.com/math-vocabulary/multiplication/multiplication) of binary numbers can be calculated using the binary multiplication rules. What is the Binary Number System? A binary number system is the base-2 [number system](https://www.splashlearn.com/math-vocabulary/number-sense/number-system). It uses only two digits, 0 and 1 to form all the numbers. Each [digit](https://www.splashlearn.com/math-vocabulary/number-sense/digit) in the binary number system is said to be a bit. If you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let’s understand the binary multiplication rules. ## Rules of Binary Multiplication Just like decimal multiplication, we define a [multiplier](https://www.splashlearn.com/math-vocabulary/multiplication/multiplier) and a multiplicand in the binary multiplication. The result of multiplication is called a product. Binary Multiplication Rules: - 0 × 0 = 0 - 0 × 1 = 0 - 1 × 0 = 0 - 1 × 1 = 1 ## Binary Multiplication Table We can create a binary multiplication table using the rules mentioned above like this: \| \| \| \| \|---\|---\|---\| \| × \| 0 \| 1 \| \| 0 \| 0 \| 0 \| \| 1 \| 0 \| 1 \| We can also summarize the rules in the binary multiplication table as: \| Multiplicand \| Multiplier \| Product \| \|---\|---\|---\| \| 0 \| 0 \| 0 × 0 = 0 \| \| 0 \| 1 \| 0 × 1 = 0 \| \| 1 \| 0 \| 1 × 0 = 0 \| \| 1 \| 1 \| 1 × 1 = 1 \| Note: When we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful. Binary Addition Rules: - 0 + 0 = 0 - 0 + 1 = 1 - 1 + 0 = 1 - 1 + 1 = 0 (carry 1) ## How to Perform Binary Multiplication Let’s understand the binary multiplication with steps. Consider the following example. Binary multiplication example: Multiply 10102 and 10112. The rules for binary multiplication are as follows: Step 1: Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (×) as we do in the decimal column multiplication method. ![Binary multiplication step 1](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-1.png) Step 2: Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number). Here, we will multiply all the digits of (1010)2 with the rightmost digit of 10112, which is 1. We call the result as the partial product. ![Binary multiplication step 2](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-2.png) Step 3: In the next row, add a placeholder of ‘0’ or ‘X’ at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two’s place). ![Binary multiplication step 3](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-3.png) Step 3: Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand. ![Binary multiplication step 4](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-step-4.png) Step 5: Finally, add all the partial products. To add all the binary numbers use the rules of binary addition. ![Binary Multiplication \&\#8211; Rules, Types, Steps, Examples, FAQs](https://lh7-us.googleusercontent.com/gPzQAD3zZM7rjrLWPsh1uje5rh29awwdqr25BAs8ELWQpJZjGCne2g7w5MEQxtwJnKY_pqj1tYKRQ2Sy4uTLJ11F6nml-ss3LgePmFUdfhXiPcKGgX-WSlD2lEKvCq53WEpp0zU8ynIGmg5QtfM3m7s) Example 2: Find the product of10012 and 1012. ![Binary multiplication of 1001 and 101](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-1001-and-101.png) ## Facts about Binary Multiplication - You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system. ## Conclusion In this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let’s use the rules and steps we learned to solve a few examples and practice problems. ## Solved Examples on Binary Multiplication 1\. Multiply (101)2 by (11)2. Verify your answer. Solution: (101)2 × (11)2 = (01111)2 ![Binary multiplication of 101 and 11](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-101-and-11.png) (101)2\= 510 (11)2 = 310 Product = 5 × 3 = 15 1510 = 11112 2\. Find the product of (110)2 by (100)2. Solution: Let’s multiply (110)2 by (100)2. ![Binary multiplication of 110 and 100](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-110-and-100.png) (110)2 × (100)2 = (11000)2 Decimal value: 6 × 4 = 24 3\. What is the product of (1101)2 by (111)2? Solution: Let’s multiply (1101)2 by (111)2. ![Binary multiplication of 1101 and 111](https://www.splashlearn.com/math-vocabulary/wp-content/uploads/2023/11/binary-multiplication-of-1101-and-111.png) (1101)2 × (111)2 = (01011011)2 Decimal value: 13 × 7 = 91 ## Practice Problems on Binary Multiplication \- 1 2 1 0 Correct answer is: 0 0 × 0 = 0 10 1 0 20 Correct answer is: 1 1 × 1 = 1 \$1\_{2}\$ \$111\_{2}\$ \$1110\_{2}\$ \$1011\_{2}\$ Correct answer is: \$1110\_{2}\$ \$111\_{2} \\times 10\_{2} = 1110\_{2}\$ \$(1111)\_{2}\$ \$(0111011)\_{2}\$ \$(1111111)\_{2}\$ \$(0111111)\_{2}\$ Correct answer is: \$(0111111)\_{2}\$ \$(1001)\_{2} \\times (111)\_{2} = (0111111)\_{2}\$ ## Frequently Asked Questions on Binary Multiplication What is the 1’s complement of a binary number? The 1’s complement of a binary number is the binary number obtained by interchanging 0 and 1. 1’s complement of 111 is 000. 1’s complement of 10101 is 010101. How does binary multiplication work? Binary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result. What are binary multiplication rules? - 0 × 0 = 0 - 0 × 1 = 0 - 1 × 0 = 0 - 1 × 1 = 1
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