Binary Arithmetic

Binary Arithmetic

As decimal numbers, the binary numbers also permit computations like addition, subtraction, multiplication and division. The following session deals only with binary addition and subtraction.

1. Binary Addition

The following table is useful when adding two binary numbers.

In 1 + 1 = 10, is considered as sum 0 and the 1 as carry bit. This carry bit is added with the previous position of the bit pattern.

Example Perform Binary addition for the following: 23₁₀ + 12₁₀

Step 1: Convert 23 and 12 into binary form

Step 2: Binary addition of 23 and 12:

2. Binary Subtraction

The table for Binary Subtraction is as follows:

When subtracting 1 from 0, borrow 1 from the next Most Significant Bit, when borrowing from the next Most Significant Bit, if it is 1, replace it with 0. If the next Most Significant Bit is 0, you must borrow from a more significant bit that contains 1 and replace it with 0 and 0s upto that point become 1s.

Example Subtract 1001010₂ – 10100₂

Example Perform binary addition for the following: (–21)₁₀ + (5)₁₀

Step 1: Change -21 and 5 into binary form

Step 2:

Step 3: 

Binary Addition of –21 and 5 :