This is my third article on binary arithmetic. In this post I am going to solve some examples on binary numbers multiplication. Here are articles on binary numbers addition and binary numbers subtraction and binary numbers division. Check out my easy to use online calculator for binary numbers to check your calculations.
Key Questions:
- How to perform multiplication on binary numbers?
- How to perform multiplication on fractional binary numbers?
- How to multiply two binary numbers?
Binary Multiplication Rules:
Binary multiplication follows very simple rules. It is a straight forward task similar to decimal multiplication. As it is binary number system, so it works with only two digits (0 and 1). The basic rules are:
| A*B | Answer |
| 0*0 | 0 |
| 0*1 | 0 |
| 1*0 | 0 |
| 1*1 | 1 |
Look at the table, the binary multiplication follows the same rules as of decimal multiplication. Like when multiplying a binary number by 0, the result is always 0. When multiplying by 1, the number remains unchanged.
Binary Multiplication Examples:
Multiplication of binary numbers and the rules of multiplication are exactly the same as we did in primary classes. I hope you don’t find anything difficult and complicated. It is easy and straightforward task. Let’s get started.
Example#01:1111)2*10)2
A = 1111)2
B = 10)2
| A | 1 | 1 | 1 | 1 | |
| B | * | 1 | 0 | ||
| 0 | 0 | 0 | 0 | ||
| 1 | 1 | 1 | 1 | X | |
| Result | 1 | 1 | 1 | 1 | 0 |
Answer: 11110)2
Example#02:11100)2*1100)2
A = 11100)2
B = 1100)2
| A | 1 | 1 | 1 | 0 | 0 | ||||
| B | * | 1 | 1 | 0 | 0 | ||||
| 0 | 0 | 0 | 0 | ||||||
| 0 | 0 | 0 | 0 | X | |||||
| 1 | 1 | 1 | 0 | 0 | X | X | |||
| 1 | 1 | 1 | 0 | 0 | X | X | X | ||
| Result | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
Answer: 101010000)2
Example#03:10011.11)2*111.11)2
| A | 1 | 0 | 0 | 1 | 1 | . | 1 | 1 | ||||
| B | * | 1 | 1 | 1 | . | 1 | 1 | |||||
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | ||||||
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | X | |||||
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | X | X | ||||
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | X | X | X | |||
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | X | X | X | X | ||
| Result | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
Answer: 10011001.0001)2
Bitwise Shifting in Binary Multiplication
In binary multiplication, multiplying a number by powers of 2 (like 2, 4, 8, etc.) is equivalent to shifting its bits to the left.
For example:
101)2 × 10)2=1010)2
Explanation:
- This is equivalent to shifting 101₂ one position to the left → 1010₂ (which is 10 in decimal).
- 101₂ (which is 5 in decimal) is multiplied by 10₂ (which is 2 in decimal).
General Rule:
- Multiplying by 2n (where n is a whole number) shifts the binary number n positions to the left.
- Each digit moves one place to the left, and a 0 is added at the end.
- Example:
- 11012×1002 (which is multiplying by 4) shifts 1101₂ two positions left. Adding two zeros at the end 110100₂
- Each left shift doubles the number.
In the decimal system, multiplying by 10 moves the digits one place to the left. For example 25 × 10 = 250. Likewise, in binary, multiplying by 2 shifts the digits left by one position. For example, 101₂ × 10₂ = 1010₂
50₁₀ x 10₁₀ = 500₁₀
This shift represents multiplication by the base value of the number system, just as in decimal arithmetic.
Lalon Sohel
Syeda Amna Ahmed