# Binary to Gray Code Converter

###### Updated: Sep 19, 2018

Binary to Gray Code Converter is used to convert a Binary number into Gray Code format. Use the Gray Code Converter tool to convert between any number base and gray code.

### Binary

Binary is the numeric system of computers. Computers are so dumb they only understand 0s and 1s. Binary numbers have a base of 2.

### Gray Code

Gray Code also known as Reflected Binary Code is an ordering of binary numeral system used for error correction in digital terrestrial television and some cable TV systems.

### Conversion from Binary to Gray Code

A Binary can be converted to Gray Code in three steps:-

1. Take the first bit of the binary input and write it to the output
2. Repeat the following steps until you reach the end of the input
3. Take the second bit of the input and XOR it to the previous bit of the input
4. Write this result to the output. So, 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1 and 1 + 1 = 0.

#### Example Binary to Gray Code Conversion

Let's say your Binary value is 10101101 and you want to convert it to it's Gray Code form.

1. Step 1: Take the first bit of the binary input and write it to the output. Output is 1
2. Step 2: Repeat the steps below until you reach the end of the input
• Take the second bit of the input and XOR it to the previous bit of the input. 1 + 0 = 1
• Write the result to the output. Output: 11
• Take the third bit of the input and XOR it to the previous bit of the input. 0 + 1 = 1
• Write the result to the output. Output: 111
• Take the fourth bit of the input and XOR it to the previous bit of the input. 1 + 0 = 1
• Write the result to the output. Output: 1111
• Take the fifth bit of the input and XOR it to the previous bit of the input. 0 + 1 = 1
• Write the result to the output. Output: 11111
• Take the sixth bit of the input and XOR it to the previous bit of the input. 1 + 1 = 0
• Write the result to the output. Output: 111110
• Take the seventh bit of the input and XOR it to the previous bit. 1 + 0 = 1
• Write the result to the output. Output: 1111101
• Take the eighth (last) bit of the input and XOR it to the previous bit. 0 + 1 = 1
• Write the result to the output. Output: 11111011
3. Step 3: So, our final gray code result is: 11111011

### Gray Code Table

DecimalHexBinaryGray Code
0000000000
1100010001
2200100011
3300110010
4401000110
5501010111
6601100101
7701110100
8810001100
9910011101
10a10101111
11b10111110
12c11001010
13d11011011
14e11101001
15f11111000