Design of Binary to Gray Code Converter Circuit

In this topic, you study how to design Binary to Gray Code Converter Circuit and draw the logic diagram.

Truth table

The conversion of 4-bit input Binary code (A B C D) into the Gray code output (W X Y Z) as shown in truth table 1. The 4-bit input so 16 (${2^4}$) combinations are possible and all of them are valid so no don’t care condition.

Table 1: Binary to Gray Code Code Converter.

Drawing of K-map for each output

From this truth table, the K-maps are drawing shown in Figure 1, to obtain a minimized expression for each output.

(a) k-map for W

(b) k-map for X

(c) k-map for Y

(d) k-map for Z

Figure 1: k-maps for Binary to Gray Code Converter.

Minimized Expression for each output

The minimized expression for each output obtained from the K-map are given below as

$W = A$

$X = \bar A B + A \bar B = A \oplus B $

$Y = \bar B C + B \bar C = B \oplus C $

$Z = \bar C D  + C \bar D = C \oplus D $

Logic Circuit Diagram

Based on the above given minimized expression for each output, a logic circuit can be drawn as shown in Figure 2.

Figure 2: Binary to Gray Code Converter logic diagram.