🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 103 (from laksa104)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa103.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.geeksforgeeks.org/maths/binary-multiplication/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.geeksforgeeks.org/maths/binary-multiplication/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.geeksforgeeks.org\/maths\/binary-multiplication\/","crawl_time":1775652883,"first_indexed_time":1750895129,"http_code":200,"src_unparsed":"org,geeksforgeeks!www,\/maths\/binary-multiplication\/ s443","src_root_hash":"12046344915360636903","history_drop_reason":null,"meta_title":"Binary Multiplication - GeeksforGeeks","meta_descriptions":["Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more.","Your All-in-One Learning Portal. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice\/competitive programming\/company interview Questions."],"attrs_boilerpipe_text":null,"attrs_markdown":"[![geeksforgeeks](https:\/\/media.geeksforgeeks.org\/gfg-gg-logo.svg)](https:\/\/www.geeksforgeeks.org\/)\n\n- Courses\n- Tutorials\n- Interview Prep\n\n- [Number System and Arithmetic](https:\/\/www.geeksforgeeks.org\/engineering-mathematics\/number-theory\/)\n- [Algebra](https:\/\/www.geeksforgeeks.org\/maths\/algebra\/)\n- [Set Theory](https:\/\/www.geeksforgeeks.org\/maths\/set-theory\/)\n- [Probability](https:\/\/www.geeksforgeeks.org\/maths\/probability-in-maths\/)\n- [Statistics](https:\/\/www.geeksforgeeks.org\/maths\/statistics\/)\n- [Geometry](https:\/\/www.geeksforgeeks.org\/maths\/geometry\/)\n- [Calculus](https:\/\/www.geeksforgeeks.org\/maths\/math-calculus\/)\n- [Logarithms](https:\/\/www.geeksforgeeks.org\/maths\/logarithms\/)\n- [Mensuration](https:\/\/www.geeksforgeeks.org\/maths\/mensuration\/)\n- [Matrices](https:\/\/www.geeksforgeeks.org\/engineering-mathematics\/matrices\/)\n- [Trigonometry](https:\/\/www.geeksforgeeks.org\/maths\/math-trigonometry\/)\n- [Mathematics](https:\/\/www.geeksforgeeks.org\/maths\/maths\/)\n\n# Binary Multiplication\nLast Updated : 23 Jul, 2025\n\n****Binary Multiplication**** is a mathematical operation that involves multiplying two binary numbers, which are numbers composed of only 0s and 1s. Binary multiplication is similar to decimal multiplication, except that the base of the number system is 2 instead of 10.\n\n- Binary multiplication involves multiplying each bit of the first number by each bit of the second number, and then adding the results.\n- Binary multiplication is fundamental in computer science and digital systems, as binary is the foundational numeral system for representing information in computers.\n\n![Binary-Multiplication](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20250521162032890772\/Binary-Multiplication.webp)\n\nBinary Multiplication\n\nIn this article, we will learn about Binary Numbers, Binary multiplication, and the rules to perform Binary multiplication, accompanied by solved examples.\n\n### ****What are Binary Numbers?****\nBinary Number is a number that is used to represent various numbers using only two symbols, “0” and “1”.\n\n- Binary numbers are expressed in the base-2 numeral system.\n- Each digit in this system is called a bit.\n\n> ****Example of a Binary Number:**** Binary of Equivalent of 6 = (110)2\n\n****Learn More,**** [****Binary Number System****](https:\/\/www.geeksforgeeks.org\/maths\/binary-number-system\/)\n\n## Binary Multiplication Rules\nBinary Multiplication is performed in the same manner as decimal numbers are multiplied. However, there are some specific rules regarding the multiplication among the binary digits 0 and 1, which we need to follow while performing the division of Binary Multiplication. Binary Multiplication rules are shown in the Binary Multiplication Table below:\n\n### Binary Multiplication Table\nThe rules for Binary Multiplication are tabulated below:\n\n| Table for Binary Multiplication Rule |   |\n|---|---|\n| Rules for Multiplication | Meaning |\n| 0 × 0 = 0 | If 0 (zero) is multiplied by another 0 (zero), then the result is 0 (zero). |\n| 0 × 1 = 0 | If 0 (zero) is multiplied by 1 (one), then the result is 0 (zero). |\n| 1 × 0 = 0 | If 1 (one) is multiplied by 0 (zero), then the result is 0 (zero). |\n| 1 × 1 = 1 | If 1 (one) is multiplied by another 1 (one), then the result is 1 (one). |\n## Binary Multiplication Calculator\nThe binary multiplication calculator added below can easily multiply two binary numbers.\n\n## How to do Binary Multiplication?\nThere are five key steps involved in Binary Multiplication:,\n\n****Step 1:**** Write the multiplicand and the multiplier one below the other, aligning the rightmost digits.\n\n****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit.\n\n****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. Write the result below the multiplier after shifting it to the left by one position.\n\n****Step 4:**** Repeat this process for each digit of the multiplier, shifting the result to the left by one more position each time.\n\n****Step 5:**** Add all the results using binary addition rules. The final sum is the product of the two binary numbers.\n\nYou can also use the Binary Multiplication Calculator to easily calculate the multiplication of two binary numbers.\n\n## Solved Question on Binary Multiplication\n****Question 1:**** (1010)2 × (101)2\n\n****Solution:****\n\n> ****Step 1:**** Write the multiplicand (1010)2 and the multiplier (101)2 one below the other, aligning the rightmost digits.  \n> ****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is.  \n> ****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position.  \n> ****Step 4:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.  \n> ****Step 5:**** Add all the results using binary addition rules. The final sum (110010)2 is the product of the two binary numbers.\n> \n> ![Binary Multiplication Example 1](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20231226181037\/Screenshot-2023-12-26-181013.png)\n> \n> So, the product of (1010)2 × (101)2 is (110010)2\n\n****Question 2:**** (1101)2 × (100)2\n\n****Solution:****\n\n> ****Step 1:**** Write the multiplicand (1101)2 and the multiplier (100)2 one below the other, aligning the rightmost digits.  \n> ****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.  \n> ****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position.  \n> ****Step 4:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.  \n> ****Step 5:**** Add all the results using binary addition rules. The final sum (110100)2 is the product of the two binary numbers.\n> \n> ![Binary Multiplication Example 2](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20231226180749\/Screenshot-2023-12-26-180719.png)\n> \n> So, the product of (1101)2 × (100)2 is (110100)2\n\n****Question 3:**** (0.101)2 × (0.11)2\n\n****Solution:****\n\n> ****Step 1:**** Write the multiplicand (0.101)2 and the multiplier (0.11)2 one below the other, aligning the rightmost digits.  \n> ****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is.  \n> ****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.  \n> ****Step 4:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions.  \n> ****Step 5:**** Add all the results using binary addition rules. The final sum (001111)2 is the product of the two binary numbers.  \n> ****Step 6:**** Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side.\n> \n> ![Binary Multiplication Example 3](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20231226180336\/Screenshot-2023-12-26-180247.png)\n> \n> So, the product of (0.101)2 × (0.11)2 is (0.01111)2\n\n****Question 4:**** (101.01)2 × (110)2\n\n****Solution:****\n\n> ****Step 1:**** Write the multiplicand (101.01)2 and the multiplier (110)2 one below the other, aligning the rightmost digits.\n> \n> ****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.\n> \n> ****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.\n> \n> ****Step 4:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.\n> \n> ****Step 5:**** Add all the results using binary addition rules. The final sum (1111110)2 is the product of the two binary numbers.\n> \n> ****Step 6:**** Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side.\n> \n> ![Binary Multiplication Example 4](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20231226175344\/Screenshot-2023-12-26-175325.png)\n> \n> So, product of (101.01)2 × (110)2 is (11111.10)2\n\n****Question 5:**** (1111)2 × (1010)2\n\n****Solution:****\n\n> ****Step 1:**** Write the multiplicand (1111)2 and the multiplier (1010)2 one below the other, aligning the rightmost digits.\n> \n> ****Step 2:**** Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.\n> \n> ****Step 3:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.\n> \n> ****Step 4:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions.\n> \n> ****Step 5:**** Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by three positions.\n> \n> ****Step 6:**** Add all the results using binary addition rules. The final sum (10010110)2 is the product of the two binary numbers.\n> \n> ![Binary Multiplication Example 5](https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20231226182931\/Screenshot-2023-12-26-182906.png)\n> \n> So, the product of (1111)2 × (1010)2 is (10010110)2\n\n****Also, check the**** [****Binary Formula****](https:\/\/www.geeksforgeeks.org\/maths\/binary-formula\/)\n\n## Binary Multiplication Practice Questions\nSome questions on Binary Multiplications are,\n\n****Question 1:**** Multiply (1110)2 by (10)2\n\n****Question 2:**** Multiply(10010101)2 by (11)2\n\n****Question 3:**** Multiply (1001)2 by (1001)2\n\n****Question 4:**** Multiply (1110010)2 by (111)2\n\n****Question 5:**** Multiply (110.10)2 by (101)2\n\nComment\n\nArticle Tags:\n\nArticle Tags:\n\n[Mathematics](https:\/\/www.geeksforgeeks.org\/category\/school-learning\/maths\/)\n\n[School Learning](https:\/\/www.geeksforgeeks.org\/category\/school-learning\/)\n\n[Geeks Premier League](https:\/\/www.geeksforgeeks.org\/category\/geeksforgeeks-initiatives\/geeks-premier-league\/)\n\n[Math-Concepts](https:\/\/www.geeksforgeeks.org\/tag\/math-concepts\/)\n\n[Geeks Premier League 2023](https:\/\/www.geeksforgeeks.org\/tag\/geeks-premier-league-2023\/)\n\n[\\+1 More]()\n### Explore\n\n[![GeeksforGeeks](https:\/\/media.geeksforgeeks.org\/auth-dashboard-uploads\/gfgFooterLogo.png)](https:\/\/www.geeksforgeeks.org\/)\n\n![location](https:\/\/media.geeksforgeeks.org\/img-practice\/Location-1685004904.svg)\n\nCorporate & Communications Address:\n\nA-143, 7th Floor, Sovereign Corporate Tower, Sector- 136, Noida, Uttar Pradesh (201305)\n\n![location](https:\/\/media.geeksforgeeks.org\/img-practice\/Location-1685004904.svg)\n\nRegistered Address:\n\nK 061, Tower K, Gulshan Vivante Apartment, Sector 137, Noida, Gautam Buddh Nagar, Uttar Pradesh, 201305\n\n[![GFG App on Play Store](https:\/\/media.geeksforgeeks.org\/auth-dashboard-uploads\/googleplay-%281%29.png)](https:\/\/geeksforgeeksapp.page.link\/gfg-app)[![GFG App on App Store](https:\/\/media.geeksforgeeks.org\/auth-dashboard-uploads\/appstore-%281%29.png)](https:\/\/geeksforgeeksapp.page.link\/gfg-app)\n\n- Company\n- [About Us](https:\/\/www.geeksforgeeks.org\/about\/)\n- [Legal](https:\/\/www.geeksforgeeks.org\/legal\/)\n- [Privacy Policy](https:\/\/www.geeksforgeeks.org\/legal\/privacy-policy\/)\n- [Contact Us](https:\/\/www.geeksforgeeks.org\/about\/contact-us\/)\n- [Advertise with us](https:\/\/www.geeksforgeeks.org\/advertise-with-us\/)\n- [GFG Corporate Solution](https:\/\/www.geeksforgeeks.org\/gfg-corporate-solution\/)\n- [Campus Training Program](https:\/\/www.geeksforgeeks.org\/campus-training-program\/)\n\n- Explore\n- [POTD](https:\/\/www.geeksforgeeks.org\/problem-of-the-day)\n- [Job-A-Thon](https:\/\/practice.geeksforgeeks.org\/events\/rec\/job-a-thon\/)\n- [Blogs](https:\/\/www.geeksforgeeks.org\/category\/blogs\/?type=recent)\n- [Nation Skill Up](https:\/\/www.geeksforgeeks.org\/nation-skill-up\/)\n\n- Tutorials\n- [Programming Languages](https:\/\/www.geeksforgeeks.org\/computer-science-fundamentals\/programming-language-tutorials\/)\n- [DSA](https:\/\/www.geeksforgeeks.org\/dsa\/dsa-tutorial-learn-data-structures-and-algorithms\/)\n- [Web Technology](https:\/\/www.geeksforgeeks.org\/web-tech\/web-technology\/)\n- [AI, ML & Data Science](https:\/\/www.geeksforgeeks.org\/machine-learning\/ai-ml-and-data-science-tutorial-learn-ai-ml-and-data-science\/)\n- [DevOps](https:\/\/www.geeksforgeeks.org\/devops\/devops-tutorial\/)\n- [CS Core Subjects](https:\/\/www.geeksforgeeks.org\/gate\/gate-exam-tutorial\/)\n- [Interview Preparation](https:\/\/www.geeksforgeeks.org\/aptitude\/interview-corner\/)\n- [Software and Tools](https:\/\/www.geeksforgeeks.org\/websites-apps\/software-and-tools-a-to-z-list\/)\n\n- Courses\n- [ML and Data Science](https:\/\/www.geeksforgeeks.org\/courses\/category\/machine-learning-data-science)\n- [DSA and Placements](https:\/\/www.geeksforgeeks.org\/courses\/category\/dsa-placements)\n- [Web Development](https:\/\/www.geeksforgeeks.org\/courses\/category\/development-testing)\n- [Programming Languages](https:\/\/www.geeksforgeeks.org\/courses\/category\/programming-languages)\n- [DevOps & Cloud](https:\/\/www.geeksforgeeks.org\/courses\/category\/cloud-devops)\n- [GATE](https:\/\/www.geeksforgeeks.org\/courses\/category\/gate)\n- [Trending Technologies](https:\/\/www.geeksforgeeks.org\/courses\/category\/trending-technologies\/)\n\n- Videos\n- [DSA](https:\/\/www.geeksforgeeks.org\/videos\/category\/sde-sheet\/)\n- [Python](https:\/\/www.geeksforgeeks.org\/videos\/category\/python\/)\n- [Java](https:\/\/www.geeksforgeeks.org\/videos\/category\/java-w6y5f4\/)\n- [C++](https:\/\/www.geeksforgeeks.org\/videos\/category\/c\/)\n- [Web Development](https:\/\/www.geeksforgeeks.org\/videos\/category\/web-development\/)\n- [Data Science](https:\/\/www.geeksforgeeks.org\/videos\/category\/data-science\/)\n- [CS Subjects](https:\/\/www.geeksforgeeks.org\/videos\/category\/cs-subjects\/)\n\n- Preparation Corner\n- [Interview Corner](https:\/\/www.geeksforgeeks.org\/interview-prep\/interview-corner\/)\n- [Aptitude](https:\/\/www.geeksforgeeks.org\/aptitude\/aptitude-questions-and-answers\/)\n- [Puzzles](https:\/\/www.geeksforgeeks.org\/aptitude\/puzzles\/)\n- [GfG 160](https:\/\/www.geeksforgeeks.org\/courses\/gfg-160-series)\n- [System Design](https:\/\/www.geeksforgeeks.org\/system-design\/system-design-tutorial\/)\n\n[@GeeksforGeeks, Sanchhaya Education Private Limited](https:\/\/www.geeksforgeeks.org\/), [All rights reserved](https:\/\/www.geeksforgeeks.org\/copyright-information\/)","attrs_readable_markdown":null,"meta_canonical":null}

3. Robots.txt Check

Query:

Response:

4. Spam/Ban Check

Query:

Response:

5. Seen Status Check

ℹ️ Skipped - page is already crawled

📄

INDEXABLE

✅

CRAWLED

2 days ago

🤖

ROBOTS ALLOWED

Page Info Filters

Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
Age cutoff	PASS	`download_stamp > now() - 6 MONTH`	0.1 months ago
History drop	PASS	`isNull(history_drop_reason)`	No drop reason
Spam/ban	PASS	`fh_dont_index != 1 AND ml_spam_score = 0`	ml_spam_score=0
Canonical	PASS	`meta_canonical IS NULL OR = '' OR = src_unparsed`	Not set

Page Details

Property	Value
URL	https://www.geeksforgeeks.org/maths/binary-multiplication/
Last Crawled	2026-04-08 12:54:43 (2 days ago)
First Indexed	2025-06-25 23:45:29 (9 months ago)
HTTP Status Code	200
Meta Title	Binary Multiplication - GeeksforGeeks
Meta Description	Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more., Your All-in-One Learning Portal. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions.
Meta Canonical	null
Boilerpipe Text	null
Markdown	[![geeksforgeeks](https://media.geeksforgeeks.org/gfg-gg-logo.svg)](https://www.geeksforgeeks.org/) - Courses - Tutorials - Interview Prep - [Number System and Arithmetic](https://www.geeksforgeeks.org/engineering-mathematics/number-theory/) - [Algebra](https://www.geeksforgeeks.org/maths/algebra/) - [Set Theory](https://www.geeksforgeeks.org/maths/set-theory/) - [Probability](https://www.geeksforgeeks.org/maths/probability-in-maths/) - [Statistics](https://www.geeksforgeeks.org/maths/statistics/) - [Geometry](https://www.geeksforgeeks.org/maths/geometry/) - [Calculus](https://www.geeksforgeeks.org/maths/math-calculus/) - [Logarithms](https://www.geeksforgeeks.org/maths/logarithms/) - [Mensuration](https://www.geeksforgeeks.org/maths/mensuration/) - [Matrices](https://www.geeksforgeeks.org/engineering-mathematics/matrices/) - [Trigonometry](https://www.geeksforgeeks.org/maths/math-trigonometry/) - [Mathematics](https://www.geeksforgeeks.org/maths/maths/) # Binary Multiplication Last Updated : 23 Jul, 2025 **Binary Multiplication is a mathematical operation that involves multiplying two binary numbers, which are numbers composed of only 0s and 1s. Binary multiplication is similar to decimal multiplication, except that the base of the number system is 2 instead of 10. - Binary multiplication involves multiplying each bit of the first number by each bit of the second number, and then adding the results. - Binary multiplication is fundamental in computer science and digital systems, as binary is the foundational numeral system for representing information in computers. ![Binary-Multiplication](https://media.geeksforgeeks.org/wp-content/uploads/20250521162032890772/Binary-Multiplication.webp) Binary Multiplication In this article, we will learn about Binary Numbers, Binary multiplication, and the rules to perform Binary multiplication, accompanied by solved examples. ### What are Binary Numbers? Binary Number is a number that is used to represent various numbers using only two symbols, “0” and “1”. - Binary numbers are expressed in the base-2 numeral system. - Each digit in this system is called a bit. > Example of a Binary Number: Binary of Equivalent of 6 = (110)2 Learn More, [Binary Number System](https://www.geeksforgeeks.org/maths/binary-number-system/) ## Binary Multiplication Rules Binary Multiplication is performed in the same manner as decimal numbers are multiplied. However, there are some specific rules regarding the multiplication among the binary digits 0 and 1, which we need to follow while performing the division of Binary Multiplication. Binary Multiplication rules are shown in the Binary Multiplication Table below: ### Binary Multiplication Table The rules for Binary Multiplication are tabulated below: \| Table for Binary Multiplication Rule \| \| \|---\|---\| \| Rules for Multiplication \| Meaning \| \| 0 × 0 = 0 \| If 0 (zero) is multiplied by another 0 (zero), then the result is 0 (zero). \| \| 0 × 1 = 0 \| If 0 (zero) is multiplied by 1 (one), then the result is 0 (zero). \| \| 1 × 0 = 0 \| If 1 (one) is multiplied by 0 (zero), then the result is 0 (zero). \| \| 1 × 1 = 1 \| If 1 (one) is multiplied by another 1 (one), then the result is 1 (one). \| ## Binary Multiplication Calculator The binary multiplication calculator added below can easily multiply two binary numbers. ## How to do Binary Multiplication? There are five key steps involved in Binary Multiplication:, Step 1: Write the multiplicand and the multiplier one below the other, aligning the rightmost digits. Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. Write the result below the multiplier after shifting it to the left by one position. Step 4: Repeat this process for each digit of the multiplier, shifting the result to the left by one more position each time. Step 5: Add all the results using binary addition rules. The final sum is the product of the two binary numbers. You can also use the Binary Multiplication Calculator to easily calculate the multiplication of two binary numbers. ## Solved Question on Binary Multiplication Question 1: (1010)2 × (101)2 Solution: > Step 1: Write the multiplicand (1010)2 and the multiplier (101)2 one below the other, aligning the rightmost digits. > Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is. > Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position. > Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions. > Step 5: Add all the results using binary addition rules. The final sum (110010)2 is the product of the two binary numbers. > > ![Binary Multiplication Example 1](https://media.geeksforgeeks.org/wp-content/uploads/20231226181037/Screenshot-2023-12-26-181013.png) > > So, the product of (1010)2 × (101)2 is (110010)2 Question 2: (1101)2 × (100)2 Solution: > Step 1: Write the multiplicand (1101)2 and the multiplier (100)2 one below the other, aligning the rightmost digits. > Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0. > Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position. > Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions. > Step 5: Add all the results using binary addition rules. The final sum (110100)2 is the product of the two binary numbers. > > ![Binary Multiplication Example 2](https://media.geeksforgeeks.org/wp-content/uploads/20231226180749/Screenshot-2023-12-26-180719.png) > > So, the product of (1101)2 × (100)2 is (110100)2 Question 3: (0.101)2 × (0.11)2 Solution: > Step 1: Write the multiplicand (0.101)2 and the multiplier (0.11)2 one below the other, aligning the rightmost digits. > Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is. > Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position. > Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions. > Step 5: Add all the results using binary addition rules. The final sum (001111)2 is the product of the two binary numbers. > Step 6: Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side. > > ![Binary Multiplication Example 3](https://media.geeksforgeeks.org/wp-content/uploads/20231226180336/Screenshot-2023-12-26-180247.png) > > So, the product of (0.101)2 × (0.11)2 is (0.01111)2 Question 4: (101.01)2 × (110)2 Solution: > Step 1: Write the multiplicand (101.01)2 and the multiplier (110)2 one below the other, aligning the rightmost digits. > > Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0. > > Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position. > > Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions. > > Step 5: Add all the results using binary addition rules. The final sum (1111110)2 is the product of the two binary numbers. > > Step 6: Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side. > > ![Binary Multiplication Example 4](https://media.geeksforgeeks.org/wp-content/uploads/20231226175344/Screenshot-2023-12-26-175325.png) > > So, product of (101.01)2 × (110)2 is (11111.10)2 Question 5: (1111)2 × (1010)2 Solution: > Step 1: Write the multiplicand (1111)2 and the multiplier (1010)2 one below the other, aligning the rightmost digits. > > Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0. > > Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position. > > Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions. > > Step 5: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by three positions. > > Step 6: Add all the results using binary addition rules. The final sum (10010110)2 is the product of the two binary numbers. > > ![Binary Multiplication Example 5](https://media.geeksforgeeks.org/wp-content/uploads/20231226182931/Screenshot-2023-12-26-182906.png) > > So, the product of (1111)2 × (1010)2 is (10010110)2 Also, check the [Binary Formula](https://www.geeksforgeeks.org/maths/binary-formula/) ## Binary Multiplication Practice Questions Some questions on Binary Multiplications are, Question 1: Multiply (1110)2 by (10)2 Question 2: Multiply(10010101)2 by (11)2 Question 3: Multiply (1001)2 by (1001)2 Question 4: Multiply (1110010)2 by (111)2 Question 5:** Multiply (110.10)2 by (101)2 Comment Article Tags: Article Tags: [Mathematics](https://www.geeksforgeeks.org/category/school-learning/maths/) [School Learning](https://www.geeksforgeeks.org/category/school-learning/) [Geeks Premier League](https://www.geeksforgeeks.org/category/geeksforgeeks-initiatives/geeks-premier-league/) [Math-Concepts](https://www.geeksforgeeks.org/tag/math-concepts/) [Geeks Premier League 2023](https://www.geeksforgeeks.org/tag/geeks-premier-league-2023/) [\+1 More]() ### Explore [![GeeksforGeeks](https://media.geeksforgeeks.org/auth-dashboard-uploads/gfgFooterLogo.png)](https://www.geeksforgeeks.org/) ![location](https://media.geeksforgeeks.org/img-practice/Location-1685004904.svg) Corporate & Communications Address: A-143, 7th Floor, Sovereign Corporate Tower, Sector- 136, Noida, Uttar Pradesh (201305) ![location](https://media.geeksforgeeks.org/img-practice/Location-1685004904.svg) Registered Address: K 061, Tower K, Gulshan Vivante Apartment, Sector 137, Noida, Gautam Buddh Nagar, Uttar Pradesh, 201305 [![GFG App on Play Store](https://media.geeksforgeeks.org/auth-dashboard-uploads/googleplay-%281%29.png)](https://geeksforgeeksapp.page.link/gfg-app)[![GFG App on App Store](https://media.geeksforgeeks.org/auth-dashboard-uploads/appstore-%281%29.png)](https://geeksforgeeksapp.page.link/gfg-app) - Company - [About Us](https://www.geeksforgeeks.org/about/) - [Legal](https://www.geeksforgeeks.org/legal/) - [Privacy Policy](https://www.geeksforgeeks.org/legal/privacy-policy/) - [Contact Us](https://www.geeksforgeeks.org/about/contact-us/) - [Advertise with us](https://www.geeksforgeeks.org/advertise-with-us/) - [GFG Corporate Solution](https://www.geeksforgeeks.org/gfg-corporate-solution/) - [Campus Training Program](https://www.geeksforgeeks.org/campus-training-program/) - Explore - [POTD](https://www.geeksforgeeks.org/problem-of-the-day) - [Job-A-Thon](https://practice.geeksforgeeks.org/events/rec/job-a-thon/) - [Blogs](https://www.geeksforgeeks.org/category/blogs/?type=recent) - [Nation Skill Up](https://www.geeksforgeeks.org/nation-skill-up/) - Tutorials - [Programming Languages](https://www.geeksforgeeks.org/computer-science-fundamentals/programming-language-tutorials/) - [DSA](https://www.geeksforgeeks.org/dsa/dsa-tutorial-learn-data-structures-and-algorithms/) - [Web Technology](https://www.geeksforgeeks.org/web-tech/web-technology/) - [AI, ML & Data Science](https://www.geeksforgeeks.org/machine-learning/ai-ml-and-data-science-tutorial-learn-ai-ml-and-data-science/) - [DevOps](https://www.geeksforgeeks.org/devops/devops-tutorial/) - [CS Core Subjects](https://www.geeksforgeeks.org/gate/gate-exam-tutorial/) - [Interview Preparation](https://www.geeksforgeeks.org/aptitude/interview-corner/) - [Software and Tools](https://www.geeksforgeeks.org/websites-apps/software-and-tools-a-to-z-list/) - Courses - [ML and Data Science](https://www.geeksforgeeks.org/courses/category/machine-learning-data-science) - [DSA and Placements](https://www.geeksforgeeks.org/courses/category/dsa-placements) - [Web Development](https://www.geeksforgeeks.org/courses/category/development-testing) - [Programming Languages](https://www.geeksforgeeks.org/courses/category/programming-languages) - [DevOps & Cloud](https://www.geeksforgeeks.org/courses/category/cloud-devops) - [GATE](https://www.geeksforgeeks.org/courses/category/gate) - [Trending Technologies](https://www.geeksforgeeks.org/courses/category/trending-technologies/) - Videos - [DSA](https://www.geeksforgeeks.org/videos/category/sde-sheet/) - [Python](https://www.geeksforgeeks.org/videos/category/python/) - [Java](https://www.geeksforgeeks.org/videos/category/java-w6y5f4/) - [C++](https://www.geeksforgeeks.org/videos/category/c/) - [Web Development](https://www.geeksforgeeks.org/videos/category/web-development/) - [Data Science](https://www.geeksforgeeks.org/videos/category/data-science/) - [CS Subjects](https://www.geeksforgeeks.org/videos/category/cs-subjects/) - Preparation Corner - [Interview Corner](https://www.geeksforgeeks.org/interview-prep/interview-corner/) - [Aptitude](https://www.geeksforgeeks.org/aptitude/aptitude-questions-and-answers/) - [Puzzles](https://www.geeksforgeeks.org/aptitude/puzzles/) - [GfG 160](https://www.geeksforgeeks.org/courses/gfg-160-series) - [System Design](https://www.geeksforgeeks.org/system-design/system-design-tutorial/) [@GeeksforGeeks, Sanchhaya Education Private Limited](https://www.geeksforgeeks.org/), [All rights reserved](https://www.geeksforgeeks.org/copyright-information/)
Readable Markdown	null
Shard	103 (laksa)
Root Hash	12046344915360636903
Unparsed URL	org,geeksforgeeks!www,/maths/binary-multiplication/ s443