# Binary to Gray Code Converter and Grey to Binary 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 2^{n-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,

That means, in 4 bit gray code, (4-1) or 3 bit code is reflected against the axis drawn after (2^{4-1})^{th} or 8^{th} row.

The bits of 4 bit gray code are considered as G_{4}G_{3}G_{2}G_{1}. Now from conversion table,
From above SOPs, let us draw K -maps for G_{4}, G_{3}, G_{2} and G_{1}.

## 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. From above gray code we get,