Decimal to Gray Converter

Use the below online conversion tool to convert any decimal number to gray code:

Decimal Number

Gray Code

Also Try:

Decimal to Binary converter

Decimal Number

Whole number, a decimal point and a fractional value combines to form a decimal number. The decimal point separates the whole number part from the fractional part of the number. Each digit of a decimal number can be any number from 0 to 9. Any value less than 1 is written to the right of decimal point. Decimal numbers are also known as base-10 number or counting numbers. Place value of decimal number varies as the whole number powers of 10 starting from the left of decimal point. Similarly, the place value of digits left to decimal point varies as the division of power of tens.

Gray code

Gray code, also known as reflected binary code, is a code having digits 0 and 1. Gray code do not have place value for its digits. Any successive codes in Gray code system have only one bit changes.

Example for decimal to gray code conversion

Let us convert 15₁₀ to gray code:
Step 1: The MSB (Most Significant Bit) of a gray code and binary code will be the same.

Step 2: The next digit of gray code will be the EXOR of the MSB and the digit right to the MSB of the binary code.

Step 3: Similarly EXOR the digit in place and the previous digit of binary code to obtain the next digit of gray code.

Step 4: Repeat the previous step till the LSB of gray code is found.

To convert decimal number to gray code, first we have to convert the number to binary.
15₁₀ = 1111₂
Now, we can convert this binary number to gray code as follows

Decimal to gray conversion table

Decimal Number	Binary Number	Gray code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111
11	1011	1110
12	1100	1010
13	1101	1011
14	1110	1001
15	1111	1000