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Gray Code to Binary Converter

Gray Code to Binary Converter is used to convert a Gray Code number into Binary 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 Gray Code numbers below (1 per line if multiple)
Binary numbers

History

  • 2018-02-05Tool Launched

Background

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.

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.

Conversion from Gray Code to Binary

A Gray Code can be converted to Binary using these steps:-

  1. Take the first bit of the gray code 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 last bit of the output
  4. Write this result to the output. So, 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1 and 1 + 1 = 0.

Example Gray Code to Binary Conversion

Let's say your Gray Code value is 11111011, and you want to convert it to its binary form.

  1. Step 1: Take the first bit of the gray code 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 last bit of the output. 1 + 1 = 0
    • Write the result to the output. Output: 10
    • Take the third bit of the input and XOR it to the last bit of the output. 1 + 0 = 1
    • Write the result to the output. Output: 101
    • Take the fourth bit of the input and XOR it to the last bit of the output. 1 + 1 = 0
    • Write the result to the output. Output: 1010
    • Take the fifth bit of the input and XOR it to the last bit of the output. 1 + 0 = 1
    • Write the result to the output. Output: 10101
    • Take the sixth bit of the input and XOR it to the last bit of the output. 0 + 1 = 1
    • Write the result to the output. Output: 101011
    • Take the seventh bit of the input and XOR it to the last bit of the output. 1 + 1 = 0
    • Write the result to the output. Output: 1010110
    • Take the eighth (last) bit of the input and XOR it to the last bit of the output. 1 + 0 = 1
    • Write the result to the output. Output: 10101101
  3. Step 3: So, our binary result is: 10101101

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