Table of Contents

Last modified on February 7th, 2024

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.

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 |

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}

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.

**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.

Last modified on February 7th, 2024