1.5 Multiplication and Division of Binary Numbers

Building upon the foundational operations of addition and subtraction, multiplication and division of binary numbers are equally critical for complex computations within digital systems. Just like their decimal counterparts, binary multiplication can often be simplified to repeated addition and shifting, while binary division involves repeated subtraction. This section will detail the algorithms and methods used to perform these operations, providing a clear understanding of how computers handle products and quotients using only 0s and 1s. Grasping these concepts is vital for a complete understanding of binary arithmetic and its application in computer architecture.

Part 1.5.1 Multiplication of Binary Numbers

To multiply binary numbers, we must understand how to multiply single binary bits.

Basic Rules of Multiplication

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

Example No. 1

Multiply 11001 by 101

Solution:

	8^th Bit	7^th Bit	6^th Bit	5^th Bit	4^th Bit	3^rd Bit	2^nd Bit	1^st Bit
Multiplicand				1	1	0	0	1
Multiplicator						1	0	1
				1	1	0	0	1
			0	0	0	0	0
		1	1	0	0	1
Summation		1	1	1	1	1	0	1

Let’s read it from left to right, the answer is: 1111101₂

Part 1.5.2 Division of Binary Numbers

To divide binary numbers, we must understand how to divide single binary bits.

0 / 1 = 0

1 / 1 = 1

Example No. 2

Divide 11011001 by 1011

Solution: