Binary Addition
Binary addition is a fundamental arithmetic operation in the binary number system. It involves adding binary digits (0 and 1) to produce a binary result. Computers use binary addition to perform calculations using digital circuits.
Binary Addition Rules
There are four basic binary addition rules:
Let’s explain binary addition rules
- 0 + 0 = 0: Adding two zeros gives zero.
- 0 + 1 = 1: Adding zero and one gives one.
- 1 + 0 = 1: Adding one and zero gives one.
- 1 + 1 = 10: Adding two ones gives zero with a carry of one to the next column.
Binary Addition Examples
There are 3 major categories of Binary Addition
Let’s explain examples of each type
1. Binary Addition without Carry Examples
Binary addition without carry occurs when adding binary digits does not produce a carry to the next column.
Example 1: Add 1-bit binary numbers
Binary addition of a single bit without carry is given in the following diagram
Example 2: Add 2-bit binary numbers
Binary addition of 01 + 10 with decimal proof is shown in the following diagram.
Example 3: Add 5-bit binary numbers
Binary addition of 10101 + 01010 with decimal proof is shown in the following diagram.
2. Binary Addition with Carry Examples
Binary addition with carry occurs when the sum of binary digits in a column is 2 or 3, requiring a carry to the next column.
Example 1: Add 1-bit binary numbers
The following diagram shows the binary addition of a single bit with carry.
Example 2: Add 2-bit binary numbers
Binary addition of 11 + 10 with decimal proof is shown in the following diagram.
Example 3: Add 5-bit binary numbers
Binary addition of 11010 + 01111 is shown in the following diagram.
3. Binary Addition with Fractions
Binary addition with fractions involves adding binary numbers that contain fractional parts separated by a binary point. The binary points must be aligned before adding the numbers. Binary addition is performed from right to left, just like decimal addition.
Binary addition with Fractions – Example 1
The following diagram shows the binary addition of the fraction: 110.10 + 011.11
Binary addition with Fractions – Example 2
The following diagram shows the binary addition of the fraction: 110.11 + 011.11
Binary addition with Fractions – Example 3
The following diagram shows the binary addition of the fraction: 110.1111 + 011.11
Binary addition with Fractions – Example 4
The following diagram shows the binary addition of the fractions: 10.1 + 011.1101
Binary Addition Summary Table
| Binary Addition Example | Example Type | Decimal Addition |
|---|---|---|
| 101101 + 010010 = 111111 | Without Carry | 45 + 18 = 63 |
| 1100101 + 0011010 = 1111111 | Without Carry | 101 + 26 = 127 |
| 10110110 + 01001001 = 11111111 | Without Carry | 182 + 73 = 255 |
| 101101 + 011011 = 1001000 | With Carry | 45 + 27 = 72 |
| 1101101 + 1011011 = 11001000 | With Carry | 109 + 91 = 200 |
| 10110110 + 01101101 = 100100011 | With Carry | 182 + 109 = 291 |
| 1011.101 + 110.011 = 10010.000 | Fraction | 11.625 + 6.375 = 18 |
| 1101.101 + 101.111 = 10011.100 | Fraction | 13.625 + 5.875 = 19.5 |
| 10110.1101 + 1101.1011 = 100100.1000 | Fraction | 22.8125 + 13.6875 = 36.5 |
| 110101.101 + 10111.011 = 1001101.000 | Fraction | 53.625 + 23.375 = 77 |
Hint: Binary Fraction to Decimal
Binary fractions use place values similar to decimal fractions, but the digits after the binary point represent negative powers of 2, such as 1/2, 1/4, 1/8, and so on. Here is a simple example of binary fraction to decimal conversion example
