014. 4-bit Binary to Gray Code Converter

4-bit Binary to Gray Code Converter

A Binary to Gray Code converter is used to transform a binary number into its equivalent Gray code. Gray code is a binary numeral system where two successive values differ in only one bit, which minimizes errors in digital systems.

Gray Code

Gray code is a binary numeral system where two successive values differ in only one bit. This property helps minimize errors in digital systems, especially during the transition between states. Gray code is commonly used in applications like error correction in digital communications, Karnaugh maps for simplifying Boolean expressions, and rotary encoders for position tracking.

Key Characteristics:

• Single Bit Change: Only one bit changes between successive values.
• Error Minimization: Reduces the chance of errors during state transitions.
• Applications: Widely used in digital systems, error correction, and position encoders.

Example of 3-bit Gray Code:

Decimal	Binary	Gray Code
0	000	000
1	001	001
2	010	011
3	011	010
4	100	110
5	101	111
6	110	101
7	111	100

Key Features:

• Error Minimization: Reduces the chance of errors during the transition between states.
• Single Bit Change: Each successive number in Gray code differs by only one bit from the previous number.

Conversion Logic

For a 4-bit binary number B3 B2 B1 B0, the equivalent Gray code G3 G2 G1 G0 is calculated as:

• G3 = B3
• G2 = B3 ⊕ B2
• G1 = B2 ⊕ B1
• G0 = B1 ⊕ B0 where ⊕ denotes the XOR operation.