How to convert Gray code to binary

Binary number

Binary numbering system uses only two symbols 0 and 1. Each digits of a binary number is referred to as bits. Binary system is also known as base -2 system. Each digit is represented by the increasing power of 2 from the LSB (Least Significant Bit). Binary system is the heart of digital electronics and is used for information flow. In digital electronics, 0 and 1 are used to denote logic states, high and low. Arithmetic operations are also possible in binary system.

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.

Gray code to binary conversion can be made easy with an example:

Let us convert 1010 from gray code to binary value:

Step 1: The MSB (Most Significant Bit) of a binary and gray code will be the same.
Binary to gray converter
Step 2: The next digit of binary will be the EXOR of the MSB of binary and the second MSB of the gray code.
Binary to gray converter
Step 3: Similarly EXOR the digit obtained in the previous step and the third MSB of gray code to obtain the third MSB of binary.
Binary to gray converter
Step 4: Repeat the previous step till the LSB of gray code is found.
Binary to gray converter

Binary corresponding to gray code 1010 is 1100.

Gray to Binary Conversion table

DecimalGrayBinary
000000000
100010001
200110010
300100011
401100100
501110101
601010110
701000111
810001100
911011001
1011111010
1111101011
1210101100
1310111101
1410011110
1510001111

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