Table of Contents
Introduction to Binary Numbers
A binary number is a number that is represented by only two digits: 0 and 1. The number 0 represents the absence of a number, while 1 represents the number itself.
Binary numbers are used in computer science to represent digital information. Each bit of information in a computer is represented by a binary number.
What is Binary Addition?
Binary addition is the addition of two binary numbers, each of which has only 0s and 1s. The sum of the two binary numbers is also a binary number.
Binary Addition Rules
Adding two binary digits, called bits, is very simple. If both bits are 0, the result is 0. If both bits are 1, the result is 1. If one bit is 0 and the other bit is 1, the result is 10 (two 1s in a row).
This rule is called the carry rule. When you add 1 and 1, the result is 10, so the 1 from the 1 + 1 gets “carried over” to the 10.
Here is an example:
01 + 01 = 10
10 + 01 = 11
Binary Addition without Regrouping
To add two binary numbers without regrouping, add the ones column and then add the tens column.
For example, +11+01=12
Binary Addition with Regrouping
To add two three-digit numbers together, we regroup the digits in the ones column and the tens column. We add the digits in the ones column and write the sum in the ones column. We add the digits in the tens column and write the sum in the tens column. We carry the one over to the hundreds column.
We add the numbers in the hundreds column and write the sum in the hundreds column. We carry the one over to the thousands column.
The final sum is the sum of the numbers in the ones column, the tens column, the hundreds column, and the thousands column.
694 + 987 = 1681
Binary Addition Examples with Solutions
There are a few different ways to solve binary addition problems.
Method 1:
Start by drawing a line under the problem, and then draw two columns. In the left column, write the numbers that are being added, and in the right column, write the sum.
Then, underneath the problem, line up the numbers in the columns and add them together.
For example, if you are asked to solve 9 + 5, you would draw two columns like this:
95 + 4
The sum is 9 + 5 = 14.
