Logic Circuits: 1-digit Decimal in Excess-3 to Gray Code Converter

Problem: Design a digital circuit that converts an Excess-3 of a single-digit decimal input into Gray Code. Draw it's logic diagram.

In order to be able to design this circuit ourselves, we need to learn Excess-3 and Gray Code. We can familiarize ourselves to them at least.

First step in designing the circuit is to generate it's Truth Table. Let's label the inputs as A, B, C, and D and outputs as W, X, Y, and Z.

Single-digit Decimal in Excess-3 to Gray Code Converter Truth Table

Based from what we've learned, Decimal 0 in Excess-3 is 0011 and Decimal 9 is 1100. Therefore, we will not care about the other outputs, thus, labeling them as Don't-cares (X). Be careful with the output as the required output is Gray Code.

Second step is finding the boolean functions of each of the outputs. Let us use Karnaugh maps (K-map). Learn about K-map through these examples here.

W = AB + ACD

X = A + BCD

Y = B'C'D' + BD + BC

Z = C'

Third step is to test the circuit manually by analysis, construction, or simulation of the circuit in some software. Here, let us simulate the circuit. If you have Proteus, download the Proteus 8 project file here (Dropbox link) for the circuit simulation.

Simulation Screenshot

Finally, we need to draw the logic diagram of our design since it is being required.

Logic Diagram of the circuit

A, B, C, and D are the inputs. W, X, Y, and Z are the outputs. If you have any question, place a comment below.