Decimal to Gray Code Converter is used to convert a Decimal number into Gray Code format. Use the Gray Code Converter tool to convert between any number base and gray code.
Output: Gray Code numbers
Convert Gray Code number to Decimal
View ToolDecimal
Decimal is the numeric system most used by us humans. It consists of the Hindu-Arabic numerals, a set of 10 digits from 0 to 9.
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 Decimal to Gray Code
A Decimal can be converted to Gray Code using these steps:-
- Convert the input decimal to binary
- Take the first bit of the binary input and write it to the output
- Repeat the following steps 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
- Write this result to the output. So,
0 + 0 = 0,0 + 1 = 1,1 + 0 = 1and1 + 1 = 0.
Example Decimal to Gray Code Conversion
Let's say your Decimal value is 173, and you want to convert it to its gray code form.
- Step 1: Convert the input decimal to binary. So,
173becomes10101101 - Step 2: Take the first bit of the binary input and write it to the output. Output is
1 - 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
- Take the second bit of the input and XOR it to the previous bit of the input.
- Step 4: 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 |
History
- Feb 5, 2018
- Tool Launched
Comments 1
George Plousos Copy Link
Hi,
I was working in a different mathematical field. Unintentionally, I discovered two ways to convert numbers to Gray code. From right to left: I make the divisions of 173 with the numbers 2,4,8,16,32, ..., 256. I round each quotient to the nearest integer. I am writing this integer down from the corresponding fraction. If this integer is even, then I write below this digit 0, otherwise I write the digit 1. These digits form the Gray Code of 173:
173
_____________________________
256 128 64 32 16 8 4 2
1 1 3 5 11 22 43 87
1 1 1 1 1 0 1 1
Faster method. I can convert all numbers that have equal lengths of digits in the binary system to Gray codes. I do this without turning any number into binary. Here I find it difficult to present this method because it contains graphs, but you can find this here:
http://viXra.org/abs/2004.0456?ref=11278286