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Binary to Gray Code Converter

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.

All processing happens on the client-side, locally in your browser. No data is uploaded.

Paste Binary numbers below (1 per line if multiple)
Gray Code numbers

History

  • 2018-02-05Tool Launched

Background

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 using these 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 its 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

Decimal Hex Binary Gray Code
0 0 0000 0000
1 1 0001 0001
2 2 0010 0011
3 3 0011 0010
4 4 0100 0110
5 5 0101 0111
6 6 0110 0101
7 7 0111 0100
8 8 1000 1100
9 9 1001 1101
10 a 1010 1111
11 b 1011 1110
12 c 1100 1010
13 d 1101 1011
14 e 1110 1001
15 f 1111 1000