Binary Arithmetic Operations (How To Do The Basics)

The binary number system utilizes just two digits, 0 and 1. This simple system allows for the representation of any number using only these digits. It supports fundamental operations like binary addition, binary subtraction, binary multiplication, or binary division.

Binary arithmetic begins with the least significant bit, which is the rightmost bit. The upcoming sections will detail each operation step-by-step.

Binary Addition

Binary addition involves four straightforward steps, outlined as follows:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 (carry 1 to the next significant bit)

An example will help us to understand the addition process. Let us take two binary numbers 10001001 and 10010101

The above example of binary arithmetic clearly explains the binary addition operation, the carried 1 is shown on the upper side of the operands.

Binary Subtraction

Here are too four simple steps to keep in memory

• 0 – 0 = 0
• 0 – 1 = 1, borrow 1 from the next more significant bit
• 1 – 0 = 1
• 1 – 1 = 0

A binary arithmetic example is given to understand the operation more clearly

The operation shows the binary subtraction clearly.

Binary Multiplication

Contrary to what one might think, binary multiplication is simpler than it appears. Here are four easy steps to multiply the binary numbers 10001001 and 10010101:

• 0×0=0
• 1×0=0
• 0×1=0
• 1×1=1 (there is no carry or borrow for this)

The arithmetic of multiplying binary numbers is shown below:

Binary Division

Binary division combines multiplication and subtraction. An illustrative example will help clarify this operation.

Here 101 is the quotient and 1 is the remainder.