Gray Code to Binary Converter

Conversion from Gray Code to Binary

A Gray Code can be converted to Binary in three 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 it's 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