Binary to Gray Code Converter

The logical circuit which converts binary code to equivalent gray code is known as binary to gray code converter. The gray code is a non weighted code. The successive gray code differs in one bit position only that means it is a unit distance code. It is also referred as cyclic code. It is not suitable for arithmetic operations. It is the most popular of the unit distance codes. It is also a reflective code. An n-bit Gray code can be obtained by reflecting an n-1 bit code about an axis after 2n-1 rows, and putting the MSB of 0 above the axis and the MSB of 1 below the axis. Reflection of Gray codes is shown below.

The 4 bits binary to gray code conversion table is given below,
4bit binary to gray conversion table

That means, in 4 bit gray code, (4-1) or 3 bit code is reflected against the axis drawn after (24-1)th or 8th row.
The bits of 4 bit gray code are considered as G4G3G2G1. Now from conversion table,

From above SOPs, let us draw K-maps for G4, G3, G2 and G1.
k-map
k-map

k-maps
k-map
logic circuit for binary to gray code converter

Grey to Binary Code Converter

In gray to binary code converter, input is a multiplies gray code and output is its equivalent binary code.
Let us consider a 4 bit gray to binary code converter. To design a 4 bit gray to binary code converter, we first have to draw a conversion table.
4bit gray to binary conversion table
k map
k map
k map
equation
k map
equation
From above Gray code we get,
logic circuit for gray to binary code converter

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