Decimal to Gray Code Converter

Updated: Sep 19, 2018

Decimal to Gray Code Converter is used to convert a Decimal number into Gray Code format

Input: Paste Decimal numbers below (1 per line if multiple)



Conversion from Decimal to Gray Code

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

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

Example Decimal to Gray Code Conversion

Let's say your Decimal value is 173 and you want to convert it to it's Gray Code form.

  1. Step 1: Convert the input decimal to binary. So, 173 becomes 10101101
  2. Step 2: Take the first bit of the binary input and write it to the output. Output is 1
  3. Step 3: 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
  4. Step 4: So, our final gray code result is: 11111011

Decimal

Decimal is the numeric system most used by us humans. It comprises of 10 digits from 0 to 9.

Gray Code

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

Gray Code Table

DecimalHexBinaryGray Code
0000000000
1100010001
2200100011
3300110010
4401000110
5501010111
6601100101
7701110100
8810001100
9910011101
10a10101111
11b10111110
12c11001010
13d11011011
14e11101001
15f11111000
 
Created: Feb 5, 2018
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