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, 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.
Binary to gray code conversion can be made easy with an example:
Let us convert a binary value of 1010 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.
Therefore 10102 is equivalent to 1111 in gray code
Decimal to binary to gray conversion table