 # Binary Multiplication

## What is Binary Multiplication?

The binary multiplication operation is actually a process of addition and shifting operation and this process has to be continued until all the multiplier is done and finally the addition operation is made. Similar to the decimal system, the multiplication of the binary numbers is done by multiplying the multiplicand with the multiplier. It is noted that the multiplication by zero makes all the bits zero and this step may be ignored in the intermediate steps and the multiplication by 1 makes all the multiplicand value unchanged. In this section, you will get answers for the questions about binary multiplication, including:

• What is Binary multiplication?
• Procedure to multiply two binary numbers
• Steps to Solve Binary multiplication using examples

## Binary Multiplication Rules

Binary multiplication, like other binary operations, is much easier, unlike the decimal multiplication when you remember the following multiplication rules. The rules of binary multiplication are:

• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 0 = 0
• 1 × 1 = 1

## Examples of Binary Multiplication

Some binary multiplication examples are given below for a better understanding of this concept.

Example 1: Solve 1010 × 101

Solution:

1010 × 101

1010

(×) 101

—————–

1010

0000

——————

01010 ……. First Intermediate Sum

1010

——————–

110010

Comparison with Decimal values:

10102 = 1010

10102 = 510

10 x 5 = 5010

(110010)2 = 5010

Another example of binary multiplication with a decimal point is as follows:

Question: 1011.01 × 110.1

Solution: Here, the decimal point is placed three places from the least significant bit. Because, the binary number 1011.01, the decimal point is 2 places from the LSB and 110.1 the decimal point is placed 1 place from the LSB.

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