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[Steps](https://mathmonks.com/number-system/binary-number-system/binary-multiplication#Steps) - [Solved Example](https://mathmonks.com/number-system/binary-number-system/binary-multiplication#Solved_Example) Last modified on February 7th, 2024 ### chapter outline - [Rules](https://mathmonks.com/number-system/binary-number-system/binary-multiplication#Rules) - [Steps](https://mathmonks.com/number-system/binary-number-system/binary-multiplication#Steps) - [Solved Example](https://mathmonks.com/number-system/binary-number-system/binary-multiplication#Solved_Example) [Home](https://mathmonks.com/) » [Arithmetic](https://mathmonks.com/arithmetic) » [Number System](https://mathmonks.com/number-system) » [Binary Number System](https://mathmonks.com/number-system/binary-number-system) » Binary Multiplication # Binary Multiplication Binary multiplication is multiplication involving 2 binary numbers. It is similar to decimal multiplication. Here, we have a multiplier and a multiplicand. The result is the product. It is nothing but repeated addition until all the multiplier is used up and the final addition is done. ## Rules The multiplication involving 2 binary numbers, 0 and 1, follows the 4 rules: | **Multiplicand** | **Multiplier** | **Product** | |---|---|---| | 0 | 0 | 0 × 0 = 0 | | 0 | 1 | 0 × 1 = 0 | | 1 | 0 | 1 × 0 = 0 | | 1 | 1 | 1 × 1 = 1 | ## Steps Multiplying 2 binary numbers involves the following steps: **Step 1**: Aligning the multiplicand and the multiplier one above the other. **Step 2**: Multiplying the multiplier’s rightmost digit or the least significant bit (LSB) with the multiplicand. **Step 3**: Placing X before multiplying the next digit of the multiplier and with the multiplicand. **Step 4**: Repeating the same process for all the multiplier digits until we reach the most significant bit (MSB), the left-most digit of the multiplicand. **Step 5**: The product obtained in each row is called the partial product. Adding all the partial products using the binary addition rules (0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10) gives the result. Let us multiply (10101)2 and (101)2 The decimal equivalent of: (10101)2 → (21)10 (101)2→ (5)10 [](https://mathmonks.com/wp-content/uploads/2024/02/Binary-Multiplication.jpg) Thus, the product of (10101)2 and (101)2 is (1101001)2 We can verify our answer by finding the decimal equivalent of (1101001)2, which is (105)10. Learn binary to decimal conversion here. Also, on multiplying the decimal equivalents of the 2 binary numbers, we get 21 × 5 = 105 This answer proves that the answer to the binary multiplication between (10101)2 and (101)2 = 105 is correct. ## Solved Example ![]()**Find the product of (11001)2 and (111)2\.** Solution: ![]() The decimal equivalent of: (11001)2 → 25 (111)2 → 7 Thus, the product of (11001)2 and (111)2 is (10101111)2 The decimal equivalent of (10101111)2 is (175)10 Also, 25 × 5 = 175Thus, the product of (11001)2 and (111)2 that is175 is correct. 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Binary multiplication is multiplication involving 2 binary numbers. It is similar to decimal multiplication. Here, we have a multiplier and a multiplicand. The result is the product. It is nothing but repeated addition until all the multiplier is used up and the final addition is done. ## Rules The multiplication involving 2 binary numbers, 0 and 1, follows the 4 rules: | **Multiplicand** | **Multiplier** | **Product** | |---|---|---| | 0 | 0 | 0 × 0 = 0 | | 0 | 1 | 0 × 1 = 0 | | 1 | 0 | 1 × 0 = 0 | | 1 | 1 | 1 × 1 = 1 | ## Steps Multiplying 2 binary numbers involves the following steps: **Step 1**: Aligning the multiplicand and the multiplier one above the other. **Step 2**: Multiplying the multiplier’s rightmost digit or the least significant bit (LSB) with the multiplicand. **Step 3**: Placing X before multiplying the next digit of the multiplier and with the multiplicand. **Step 4**: Repeating the same process for all the multiplier digits until we reach the most significant bit (MSB), the left-most digit of the multiplicand. **Step 5**: The product obtained in each row is called the partial product. Adding all the partial products using the binary addition rules (0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10) gives the result. Let us multiply (10101)2 and (101)2 The decimal equivalent of: (10101)2 → (21)10 (101)2→ (5)10 [](https://mathmonks.com/wp-content/uploads/2024/02/Binary-Multiplication.jpg) Thus, the product of (10101)2 and (101)2 is (1101001)2 We can verify our answer by finding the decimal equivalent of (1101001)2, which is (105)10. Learn binary to decimal conversion here. Also, on multiplying the decimal equivalents of the 2 binary numbers, we get 21 × 5 = 105 This answer proves that the answer to the binary multiplication between (10101)2 and (101)2 = 105 is correct. ## Solved Example **Find the product of (11001)2 and (111)2\.** Solution: The decimal equivalent of: (11001)2 → 25 (111)2 → 7 Thus, the product of (11001)2 and (111)2 is (10101111)2 The decimal equivalent of (10101111)2 is (175)10 Also, 25 × 5 = 175Thus, the product of (11001)2 and (111)2 that is175 is correct.