🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 147 (from laksa081)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa147.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, ml_categories_json AS ml_categories_json, ml_types_json AS ml_types_json, ml_intent_types_json AS ml_intent_types_json, meta_language AS meta_language, attrs_author AS attrs_author, ifNull(toUnixTimestamp(attrs_publish_time), 0) AS attrs_publish_time, ifNull(toUnixTimestamp(attrs_original_publish_time), 0) AS attrs_original_publish_time, ifNull(attrs_is_republished, 0) AS attrs_is_republished, ifNull(attrs_nr_words, 0) AS attrs_nr_words, ifNull(attrs_boilerpipe_nr_words, 0) AS attrs_boilerpipe_nr_words, ifNull(body_ext_links_number, 0) AS body_ext_links_number, ifNull(body_int_links_number, 0) AS body_int_links_number, ifNull(meta_nofollow, 0) AS meta_nofollow, ifNull(meta_noarchive, 0) AS meta_noarchive, ifNull(props_was_rendered, 0) AS props_was_rendered, ifNull(src_redirect, \'\') AS src_redirect, ifNull(download_time_msec, 0) AS download_time_msec, ifNull(download_ttfb_msec, 0) AS download_ttfb_msec, ifNull(download_size, 0) AS download_size FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.math-only-math.com/binary-multiplication.html\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.math-only-math.com/binary-multiplication.html\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.math-only-math.com\/binary-multiplication.html","crawl_time":1776521742,"first_indexed_time":1540062164,"http_code":200,"src_unparsed":"com,math-only-math!www,\/binary-multiplication.html s443","src_root_hash":"14917645262318970347","history_drop_reason":null,"meta_title":"Binary Multiplication | Process of Multiplication of Binary Numbers | Examples","meta_descriptions":["The procedure for binary multiplication is similar to that in decimal system. As in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one"],"attrs_boilerpipe_text":"Subscribe to our\n▶️ \nYouTube channel\n \n🔴\nfor the latest videos, updates, and tips.\nThe procedure\nfor binary multiplication is similar to that in decimal system.\nThe rules of binary multiplication are given\nby the following table:\n×\n1\n0\n1\n1\n0\n0\n0\n0\nAs in decimal\nsystem, the multiplication of binary numbers is carried out by multiplying the\nmultiplicand by one bit of the multiplier at a time and the result of the\npartial product for each bit is placed in such a manner that the LSB is under\nthe corresponding multiplier bit.\nFinally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted.\nThe binary point in the product is then\nplaced before this total number of places counted from right. It should be\nnoted that a multiplication by zero makes all the bits of the partial product\nzero and may thus be ignored in intermediate steps.\nAlso, a multiplication by 1 leaves the bits of multiplicand unchanged\nbut shifts it towards the left by one bit position. The multiplication of\nbinary numbers becomes more convenient by carrying out intermediate sums of\npartial products.\nIn the case of binary\nmultiplication there are certain advantages. The multiplication is\nactually the addition of multiplicand with itself after some suitable shift\ndepending upon the multiplier. Thus multiplication is actually a process of\nshifting and adding. This process is to be continued until the shifting due to\nMSB of the multiplier is done and final addition is made.\nA\nfew examples will make the process of\nbinary\nmultiplication clear:\nMultiply:\n(i) 10111 by 1101\nSolution:\n                                1 0 1 1 1\n          1 1 0 1\n                                 1 0 1 1 1           \n←\nFirst partial product\n      1 0 1 1 1     \n                            1 1 1 0 0 1 1           \n←\nFirst intermediate sum\n      1 0 1 1 1          \n                       1 0 0 1 0 1 0 1 1           \n←\nFinal sum.\nHence the required product is\n100101011.\n(ii) 11011.101 by 101.111\n                                        1 1 0 1 1 . 1 0 1\n          1 0 1 . 1 1 1  \n                                        1 1 0 1 1 . 1 0 1\n    1 1 0 1 1 1 . 0 1    \n←\nFirst partial product\n                                 \n1 0 1 0 0 1 0   1 1 1        \n←\nFirst intermediate sum\n    1 1 0 1 1 1 0   1        \n                               1 1 0 0 0 0 0 1   0 1 1    \n←\nSecond intermediate sum\n    1 1 0 1 1 1 0 1              \n                             1 1 0 0 1 1 1 1 0   0 1 1        \n←\nThird intermediate sum\n    1 1 0 1 1 1 0 1                    \n                       1 0 1 0 0 0 1 0 0 1 0   0 1 1\nHence the required result is\n10100010.010011.\n●\nBinary Numbers\nData and\nInformation\nNumber\nSystem\nDecimal\nNumber System\nBinary\nNumber System\nWhy Binary\nNumbers are Used\nBinary to\nDecimal Conversion\nConversion\nof Numbers\nOctal Number System\nHexa-decimal Number System\nConversion\nof Binary Numbers to Octal or Hexa-decimal Numbers\nOctal and\nHexa-Decimal Numbers\nSigned-magnitude\nRepresentation\nRadix Complement\nDiminished Radix Complement\nArithmetic\nOperations of Binary Numbers\nBinary Addition\nBinary Subtraction\nSubtraction\nby 2’s Complement\nSubtraction\nby 1’s Complement\nAddition and Subtraction of Binary Numbers\nBinary Addition using 1’s Complement\nBinary Addition using 2’s Complement\nBinary Multiplication\nBinary Division\nAddition\nand Subtraction of Octal Numbers\nMultiplication\nof Octal Numbers\nHexadecimal Addition and Subtraction\nFrom Binary Multiplication to HOME PAGE\nDidn't find what you were looking for? Or want to know more information\nabout\nMath Only Math\n.\nUse this Google Search to find what you need.\nNew!\nComments\nHave your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.\nShare this page:\nWhat’s this?\nFacebook\nX\nPinterest\nWhatsApp\nReddit\nShare\nFacebook\nX\nPinterest\nWhatsApp\nReddit","attrs_markdown":"[Math Only Math](https:\/\/www.math-only-math.com\/)\n\nLearn math step-by-step.\n\nSubscribe to our ▶️ [**YouTube channel**](https:\/\/www.youtube.com\/channel\/UCvVgXqKrxxcLfefLJQpyQlw?sub_confirmation=1) 🔴 for the latest videos, updates, and tips.\n\n# Binary Multiplication\nThe procedure for binary multiplication is similar to that in decimal system.\n\n**The rules of binary multiplication are given by the following table:**\n\n|   |   |   |\n|---|---|---|\n| × | 1 | 0 |\n| 1 | 1 | 0 |\n| 0 | 0 | 0 |\n\nAs in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit.\n\nFinally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted.\n\nThe binary point in the product is then placed before this total number of places counted from right. It should be noted that a multiplication by zero makes all the bits of the partial product zero and may thus be ignored in intermediate steps.\n\nAlso, a multiplication by 1 leaves the bits of multiplicand unchanged but shifts it towards the left by one bit position. The multiplication of binary numbers becomes more convenient by carrying out intermediate sums of partial products.\n\nIn the case of binary multiplication there are certain advantages. The multiplication is actually the addition of multiplicand with itself after some suitable shift depending upon the multiplier. Thus multiplication is actually a process of shifting and adding. This process is to be continued until the shifting due to MSB of the multiplier is done and final addition is made.\n\n**A few examples will make the process of** **binary multiplication clear:**\n\n**Multiply:**\n\n**(i) 10111 by 1101**\n\n**Solution:**\n\n1 0 1 1 1\n\n1 1 0 1\n\n1 0 1 1 1\n\n←\n\nFirst partial product\n\n1 0 1 1 1\n\n1 1 1 0 0 1 1\n\n←\n\nFirst intermediate sum\n\n1 0 1 1 1\n\n1 0 0 1 0 1 0 1 1\n\n←\n\nFinal sum.\n\n**Hence the required product is 100101011.**\n\n**(ii) 11011.101 by 101.111**\n\n1 1 0 1 1 . 1 0 1\n\n1 0 1 . 1 1 1\n\n1 1 0 1 1 . 1 0 1\n\n1 1 0 1 1 1 . 0 1\n\n←\n\nFirst partial product  \n  \n 1 0 1 0 0 1 0 1 1 1\n\n←\n\nFirst intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 1 0 0 0 0 0 1 0 1 1\n\n←\n\nSecond intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 1 0 0 1 1 1 1 0 0 1 1\n\n←\n\nThird intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 0 1 0 0 0 1 0 0 1 0 0 1 1\n\n**Hence the required result is 10100010.010011.**\n\n● [**Binary Numbers**](https:\/\/www.math-only-math.com\/binary-numbers.html)\n\n- [**Data and Information**](https:\/\/www.math-only-math.com\/data-and-information.html)\n\n- [**Number System**](https:\/\/www.math-only-math.com\/number-system.html)\n\n[**Decimal Number System**](https:\/\/www.math-only-math.com\/decimal-number-system.html)\n\n- **[Binary Number System](https:\/\/www.math-only-math.com\/binary-number-system.html)**\n\n[**Why Binary Numbers are Used**](https:\/\/www.math-only-math.com\/why-binary-numbers-are-used.html) [**Binary to Decimal Conversion**](https:\/\/www.math-only-math.com\/binary-to-decimal-conversion.html) [**Conversion of Numbers**](https:\/\/www.math-only-math.com\/conversion-of-numbers.html)\n\n- **[Octal Number System](https:\/\/www.math-only-math.com\/octal-number-system.html)**\n\n[**Hexa-decimal Number System**](https:\/\/www.math-only-math.com\/hexa-decimal-number-system.html) [**Conversion of Binary Numbers to Octal or Hexa-decimal Numbers**](https:\/\/www.math-only-math.com\/conversion-of-binary-numbers-to-octal-or-hexa-decimal-numbers.html) [**Octal and Hexa-Decimal Numbers**](https:\/\/www.math-only-math.com\/octal-and-hexa-decimal-numbers.html) [**Signed-magnitude Representation**](https:\/\/www.math-only-math.com\/signed-magnitude-representation.html) [**Radix Complement**](https:\/\/www.math-only-math.com\/radix-complement.html) [**Diminished Radix Complement**](https:\/\/www.math-only-math.com\/diminished-radix-complement.html) [**Arithmetic Operations of Binary Numbers**](https:\/\/www.math-only-math.com\/arithmetic-operations-of-binary-numbers.html)\n\n- **[Binary Addition](https:\/\/www.math-only-math.com\/binary-addition.html)**\n\n- **[Binary Subtraction](https:\/\/www.math-only-math.com\/binary-subtraction.html)**\n\n- **[Subtraction by 2’s Complement](https:\/\/www.math-only-math.com\/subtraction-by-2s-complement.html)**\n\n- **[Subtraction by 1’s Complement](https:\/\/www.math-only-math.com\/subtraction-by-1s-complement.html)**\n\n- **[Addition and Subtraction of Binary Numbers](https:\/\/www.math-only-math.com\/addition-and-subtraction-of-binary-numbers.html)**\n\n- **[Binary Addition using 1’s Complement](https:\/\/www.math-only-math.com\/binary-addition-using-1s-complement.html)**\n\n- **[Binary Addition using 2’s Complement](https:\/\/www.math-only-math.com\/binary-addition-using-2s-complement.html)**\n\n- **[Binary Multiplication](https:\/\/www.math-only-math.com\/binary-multiplication.html)**\n\n- **[Binary Division](https:\/\/www.math-only-math.com\/binary-division.html)**\n\n- **[Addition and Subtraction of Octal Numbers](https:\/\/www.math-only-math.com\/addition-and-subtraction-of-octal-numbers.html)**\n\n- **[Multiplication of Octal Numbers](https:\/\/www.math-only-math.com\/multiplication-of-octal-numbers.html)**\n\n- **[Hexadecimal Addition and Subtraction](https:\/\/www.math-only-math.com\/hexadecimal-addition-and-subtraction.html)**\n\n[**From Binary Multiplication to HOME PAGE**](https:\/\/www.math-only-math.com\/)\n\nDidn't find what you were looking for? 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All Rights Reserved. 2010 - 2026.**](https:\/\/www.math-only-math.com\/)","attrs_readable_markdown":"Subscribe to our ▶️ [**YouTube channel**](https:\/\/www.youtube.com\/channel\/UCvVgXqKrxxcLfefLJQpyQlw?sub_confirmation=1) 🔴 for the latest videos, updates, and tips.\n\nThe procedure for binary multiplication is similar to that in decimal system.\n\n**The rules of binary multiplication are given by the following table:**\n\n|   |   |   |\n|---|---|---|\n| × | 1 | 0 |\n| 1 | 1 | 0 |\n| 0 | 0 | 0 |\n\nAs in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit.\n\nFinally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted.\n\nThe binary point in the product is then placed before this total number of places counted from right. It should be noted that a multiplication by zero makes all the bits of the partial product zero and may thus be ignored in intermediate steps.\n\nAlso, a multiplication by 1 leaves the bits of multiplicand unchanged but shifts it towards the left by one bit position. The multiplication of binary numbers becomes more convenient by carrying out intermediate sums of partial products.\n\nIn the case of binary multiplication there are certain advantages. The multiplication is actually the addition of multiplicand with itself after some suitable shift depending upon the multiplier. Thus multiplication is actually a process of shifting and adding. This process is to be continued until the shifting due to MSB of the multiplier is done and final addition is made.\n\n**A few examples will make the process of** **binary multiplication clear:**\n\n**Multiply:**\n\n**(i) 10111 by 1101**\n\n**Solution:**\n\n1 0 1 1 1\n\n1 1 0 1\n\n1 0 1 1 1\n\n← First partial product\n\n1 0 1 1 1\n\n1 1 1 0 0 1 1\n\n← First intermediate sum\n\n1 0 1 1 1\n\n1 0 0 1 0 1 0 1 1\n\n← Final sum.\n\n**Hence the required product is 100101011.**\n\n**(ii) 11011.101 by 101.111**\n\n1 1 0 1 1 . 1 0 1\n\n1 0 1 . 1 1 1\n\n1 1 0 1 1 . 1 0 1\n\n1 1 0 1 1 1 . 0 1\n\n← First partial product\n\n1 0 1 0 0 1 0 1 1 1\n\n← First intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 1 0 0 0 0 0 1 0 1 1\n\n← Second intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 1 0 0 1 1 1 1 0 0 1 1\n\n← Third intermediate sum\n\n1 1 0 1 1 1 0 1\n\n1 0 1 0 0 0 1 0 0 1 0 0 1 1\n\n**Hence the required result is 10100010.010011.**\n\n● [**Binary Numbers**](https:\/\/www.math-only-math.com\/binary-numbers.html)\n\n- [**Data and Information**](https:\/\/www.math-only-math.com\/data-and-information.html)\n\n[**Number System**](https:\/\/www.math-only-math.com\/number-system.html)[**Decimal Number System**](https:\/\/www.math-only-math.com\/decimal-number-system.html)**[Binary Number System](https:\/\/www.math-only-math.com\/binary-number-system.html)**[**Why Binary Numbers are Used**](https:\/\/www.math-only-math.com\/why-binary-numbers-are-used.html) [**Binary to Decimal Conversion**](https:\/\/www.math-only-math.com\/binary-to-decimal-conversion.html) [**Conversion of Numbers**](https:\/\/www.math-only-math.com\/conversion-of-numbers.html)**[Octal Number System](https:\/\/www.math-only-math.com\/octal-number-system.html)**[**Hexa-decimal Number System**](https:\/\/www.math-only-math.com\/hexa-decimal-number-system.html) [**Conversion of Binary Numbers to Octal or Hexa-decimal Numbers**](https:\/\/www.math-only-math.com\/conversion-of-binary-numbers-to-octal-or-hexa-decimal-numbers.html) [**Octal and Hexa-Decimal Numbers**](https:\/\/www.math-only-math.com\/octal-and-hexa-decimal-numbers.html) [**Signed-magnitude Representation**](https:\/\/www.math-only-math.com\/signed-magnitude-representation.html) [**Radix Complement**](https:\/\/www.math-only-math.com\/radix-complement.html) [**Diminished Radix Complement**](https:\/\/www.math-only-math.com\/diminished-radix-complement.html) [**Arithmetic Operations of Binary Numbers**](https:\/\/www.math-only-math.com\/arithmetic-operations-of-binary-numbers.html)**[Binary Addition](https:\/\/www.math-only-math.com\/binary-addition.html)** **[Binary Subtraction](https:\/\/www.math-only-math.com\/binary-subtraction.html)** **[Subtraction by 2’s Complement](https:\/\/www.math-only-math.com\/subtraction-by-2s-complement.html)** **[Subtraction by 1’s Complement](https:\/\/www.math-only-math.com\/subtraction-by-1s-complement.html)** **[Addition and Subtraction of Binary Numbers](https:\/\/www.math-only-math.com\/addition-and-subtraction-of-binary-numbers.html)** **[Binary Addition using 1’s Complement](https:\/\/www.math-only-math.com\/binary-addition-using-1s-complement.html)** **[Binary Addition using 2’s Complement](https:\/\/www.math-only-math.com\/binary-addition-using-2s-complement.html)** **[Binary Multiplication](https:\/\/www.math-only-math.com\/binary-multiplication.html)** **[Binary Division](https:\/\/www.math-only-math.com\/binary-division.html)** **[Addition and Subtraction of Octal Numbers](https:\/\/www.math-only-math.com\/addition-and-subtraction-of-octal-numbers.html)** **[Multiplication of Octal Numbers](https:\/\/www.math-only-math.com\/multiplication-of-octal-numbers.html)** **[Hexadecimal Addition and Subtraction](https:\/\/www.math-only-math.com\/hexadecimal-addition-and-subtraction.html)**\n\n[**From Binary Multiplication to HOME PAGE**](https:\/\/www.math-only-math.com\/)\n\nDidn't find what you were looking for? 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Meta Title	Binary Multiplication \| Process of Multiplication of Binary Numbers \| Examples
Meta Description	The procedure for binary multiplication is similar to that in decimal system. As in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one
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Boilerpipe Text	Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips. The procedure for binary multiplication is similar to that in decimal system. The rules of binary multiplication are given by the following table: × 1 0 1 1 0 0 0 0 As in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit. Finally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted. The binary point in the product is then placed before this total number of places counted from right. It should be noted that a multiplication by zero makes all the bits of the partial product zero and may thus be ignored in intermediate steps. Also, a multiplication by 1 leaves the bits of multiplicand unchanged but shifts it towards the left by one bit position. The multiplication of binary numbers becomes more convenient by carrying out intermediate sums of partial products. In the case of binary multiplication there are certain advantages. The multiplication is actually the addition of multiplicand with itself after some suitable shift depending upon the multiplier. Thus multiplication is actually a process of shifting and adding. This process is to be continued until the shifting due to MSB of the multiplier is done and final addition is made. A few examples will make the process of binary multiplication clear: Multiply: (i) 10111 by 1101 Solution: 1 0 1 1 1 1 1 0 1 1 0 1 1 1 ← First partial product 1 0 1 1 1 1 1 1 0 0 1 1 ← First intermediate sum 1 0 1 1 1 1 0 0 1 0 1 0 1 1 ← Final sum. Hence the required product is 100101011. (ii) 11011.101 by 101.111 1 1 0 1 1 . 1 0 1 1 0 1 . 1 1 1 1 1 0 1 1 . 1 0 1 1 1 0 1 1 1 . 0 1 ← First partial product 1 0 1 0 0 1 0 1 1 1 ← First intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 ← Second intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 ← Third intermediate sum 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 Hence the required result is 10100010.010011. ● Binary Numbers Data and Information Number System Decimal Number System Binary Number System Why Binary Numbers are Used Binary to Decimal Conversion Conversion of Numbers Octal Number System Hexa-decimal Number System Conversion of Binary Numbers to Octal or Hexa-decimal Numbers Octal and Hexa-Decimal Numbers Signed-magnitude Representation Radix Complement Diminished Radix Complement Arithmetic Operations of Binary Numbers Binary Addition Binary Subtraction Subtraction by 2’s Complement Subtraction by 1’s Complement Addition and Subtraction of Binary Numbers Binary Addition using 1’s Complement Binary Addition using 2’s Complement Binary Multiplication Binary Division Addition and Subtraction of Octal Numbers Multiplication of Octal Numbers Hexadecimal Addition and Subtraction From Binary Multiplication to HOME PAGE Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need. New! Comments Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question. Share this page: What’s this? Facebook X Pinterest WhatsApp Reddit Share Facebook X Pinterest WhatsApp Reddit
Markdown	[Math Only Math](https://www.math-only-math.com/) Learn math step-by-step. Subscribe to our ▶️ [YouTube channel](https://www.youtube.com/channel/UCvVgXqKrxxcLfefLJQpyQlw?sub_confirmation=1) 🔴 for the latest videos, updates, and tips. # Binary Multiplication The procedure for binary multiplication is similar to that in decimal system. The rules of binary multiplication are given by the following table: \| \| \| \| \|---\|---\|---\| \| × \| 1 \| 0 \| \| 1 \| 1 \| 0 \| \| 0 \| 0 \| 0 \| As in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit. Finally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted. The binary point in the product is then placed before this total number of places counted from right. It should be noted that a multiplication by zero makes all the bits of the partial product zero and may thus be ignored in intermediate steps. Also, a multiplication by 1 leaves the bits of multiplicand unchanged but shifts it towards the left by one bit position. The multiplication of binary numbers becomes more convenient by carrying out intermediate sums of partial products. In the case of binary multiplication there are certain advantages. The multiplication is actually the addition of multiplicand with itself after some suitable shift depending upon the multiplier. Thus multiplication is actually a process of shifting and adding. This process is to be continued until the shifting due to MSB of the multiplier is done and final addition is made. A few examples will make the process of binary multiplication clear: Multiply: (i) 10111 by 1101 Solution: 1 0 1 1 1 1 1 0 1 1 0 1 1 1 ← First partial product 1 0 1 1 1 1 1 1 0 0 1 1 ← First intermediate sum 1 0 1 1 1 1 0 0 1 0 1 0 1 1 ← Final sum. Hence the required product is 100101011. (ii) 11011.101 by 101.111 1 1 0 1 1 . 1 0 1 1 0 1 . 1 1 1 1 1 0 1 1 . 1 0 1 1 1 0 1 1 1 . 0 1 ← First partial product 1 0 1 0 0 1 0 1 1 1 ← First intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 ← Second intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 ← Third intermediate sum 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 Hence the required result is 10100010.010011. ● [Binary Numbers](https://www.math-only-math.com/binary-numbers.html) - [Data and Information](https://www.math-only-math.com/data-and-information.html) - [Number System](https://www.math-only-math.com/number-system.html) [Decimal Number System](https://www.math-only-math.com/decimal-number-system.html) - [Binary Number System](https://www.math-only-math.com/binary-number-system.html) [Why Binary Numbers are Used](https://www.math-only-math.com/why-binary-numbers-are-used.html) [Binary to Decimal Conversion](https://www.math-only-math.com/binary-to-decimal-conversion.html) [Conversion of Numbers](https://www.math-only-math.com/conversion-of-numbers.html) - [Octal Number System](https://www.math-only-math.com/octal-number-system.html) [Hexa-decimal Number System](https://www.math-only-math.com/hexa-decimal-number-system.html) [Conversion of Binary Numbers to Octal or Hexa-decimal Numbers](https://www.math-only-math.com/conversion-of-binary-numbers-to-octal-or-hexa-decimal-numbers.html) [Octal and Hexa-Decimal Numbers](https://www.math-only-math.com/octal-and-hexa-decimal-numbers.html) [Signed-magnitude Representation](https://www.math-only-math.com/signed-magnitude-representation.html) [Radix Complement](https://www.math-only-math.com/radix-complement.html) [Diminished Radix Complement](https://www.math-only-math.com/diminished-radix-complement.html) [Arithmetic Operations of Binary Numbers](https://www.math-only-math.com/arithmetic-operations-of-binary-numbers.html) - [Binary Addition](https://www.math-only-math.com/binary-addition.html) - [Binary Subtraction](https://www.math-only-math.com/binary-subtraction.html) - [Subtraction by 2’s Complement](https://www.math-only-math.com/subtraction-by-2s-complement.html) - [Subtraction by 1’s Complement](https://www.math-only-math.com/subtraction-by-1s-complement.html) - [Addition and Subtraction of Binary Numbers](https://www.math-only-math.com/addition-and-subtraction-of-binary-numbers.html) - [Binary Addition using 1’s Complement](https://www.math-only-math.com/binary-addition-using-1s-complement.html) - [Binary Addition using 2’s Complement](https://www.math-only-math.com/binary-addition-using-2s-complement.html) - [Binary Multiplication](https://www.math-only-math.com/binary-multiplication.html) - [Binary Division](https://www.math-only-math.com/binary-division.html) - [Addition and Subtraction of Octal Numbers](https://www.math-only-math.com/addition-and-subtraction-of-octal-numbers.html) - [Multiplication of Octal Numbers](https://www.math-only-math.com/multiplication-of-octal-numbers.html) - [Hexadecimal Addition and Subtraction](https://www.math-only-math.com/hexadecimal-addition-and-subtraction.html) [From Binary Multiplication to HOME PAGE](https://www.math-only-math.com/) Didn't find what you were looking for? 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Readable Markdown	Subscribe to our ▶️ [YouTube channel](https://www.youtube.com/channel/UCvVgXqKrxxcLfefLJQpyQlw?sub_confirmation=1) 🔴 for the latest videos, updates, and tips. The procedure for binary multiplication is similar to that in decimal system. The rules of binary multiplication are given by the following table: \| \| \| \| \|---\|---\|---\| \| × \| 1 \| 0 \| \| 1 \| 1 \| 0 \| \| 0 \| 0 \| 0 \| As in decimal system, the multiplication of binary numbers is carried out by multiplying the multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit. Finally the partial products are added to get the complete product. The placement of the binary point in the product of two binary numbers having fractional representation is determined in the same way as in the product of decimal numbers with fractional representation. The total number of places after the binary point in the multiplicand and the multiplier is counted. The binary point in the product is then placed before this total number of places counted from right. It should be noted that a multiplication by zero makes all the bits of the partial product zero and may thus be ignored in intermediate steps. Also, a multiplication by 1 leaves the bits of multiplicand unchanged but shifts it towards the left by one bit position. The multiplication of binary numbers becomes more convenient by carrying out intermediate sums of partial products. In the case of binary multiplication there are certain advantages. The multiplication is actually the addition of multiplicand with itself after some suitable shift depending upon the multiplier. Thus multiplication is actually a process of shifting and adding. This process is to be continued until the shifting due to MSB of the multiplier is done and final addition is made. A few examples will make the process of binary multiplication clear: Multiply: (i) 10111 by 1101 Solution: 1 0 1 1 1 1 1 0 1 1 0 1 1 1 ← First partial product 1 0 1 1 1 1 1 1 0 0 1 1 ← First intermediate sum 1 0 1 1 1 1 0 0 1 0 1 0 1 1 ← Final sum. Hence the required product is 100101011. (ii) 11011.101 by 101.111 1 1 0 1 1 . 1 0 1 1 0 1 . 1 1 1 1 1 0 1 1 . 1 0 1 1 1 0 1 1 1 . 0 1 ← First partial product 1 0 1 0 0 1 0 1 1 1 ← First intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 ← Second intermediate sum 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 ← Third intermediate sum 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 Hence the required result is 10100010.010011. ● [Binary Numbers](https://www.math-only-math.com/binary-numbers.html) - [Data and Information](https://www.math-only-math.com/data-and-information.html) [Number System](https://www.math-only-math.com/number-system.html)[Decimal Number System](https://www.math-only-math.com/decimal-number-system.html)[Binary Number System](https://www.math-only-math.com/binary-number-system.html)[Why Binary Numbers are Used](https://www.math-only-math.com/why-binary-numbers-are-used.html) [Binary to Decimal Conversion](https://www.math-only-math.com/binary-to-decimal-conversion.html) [Conversion of Numbers](https://www.math-only-math.com/conversion-of-numbers.html)[Octal Number System](https://www.math-only-math.com/octal-number-system.html)[Hexa-decimal Number System](https://www.math-only-math.com/hexa-decimal-number-system.html) [Conversion of Binary Numbers to Octal or Hexa-decimal Numbers](https://www.math-only-math.com/conversion-of-binary-numbers-to-octal-or-hexa-decimal-numbers.html) [Octal and Hexa-Decimal Numbers](https://www.math-only-math.com/octal-and-hexa-decimal-numbers.html) [Signed-magnitude Representation](https://www.math-only-math.com/signed-magnitude-representation.html) [Radix Complement](https://www.math-only-math.com/radix-complement.html) [Diminished Radix Complement](https://www.math-only-math.com/diminished-radix-complement.html) [Arithmetic Operations of Binary Numbers](https://www.math-only-math.com/arithmetic-operations-of-binary-numbers.html)[Binary Addition](https://www.math-only-math.com/binary-addition.html) [Binary Subtraction](https://www.math-only-math.com/binary-subtraction.html) [Subtraction by 2’s Complement](https://www.math-only-math.com/subtraction-by-2s-complement.html) [Subtraction by 1’s Complement](https://www.math-only-math.com/subtraction-by-1s-complement.html) [Addition and Subtraction of Binary Numbers](https://www.math-only-math.com/addition-and-subtraction-of-binary-numbers.html) [Binary Addition using 1’s Complement](https://www.math-only-math.com/binary-addition-using-1s-complement.html) [Binary Addition using 2’s Complement](https://www.math-only-math.com/binary-addition-using-2s-complement.html) [Binary Multiplication](https://www.math-only-math.com/binary-multiplication.html) [Binary Division](https://www.math-only-math.com/binary-division.html) [Addition and Subtraction of Octal Numbers](https://www.math-only-math.com/addition-and-subtraction-of-octal-numbers.html) [Multiplication of Octal Numbers](https://www.math-only-math.com/multiplication-of-octal-numbers.html) [Hexadecimal Addition and Subtraction](https://www.math-only-math.com/hexadecimal-addition-and-subtraction.html) [From Binary Multiplication to HOME PAGE](https://www.math-only-math.com/) Didn't find what you were looking for? 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