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In: Electrical Engineering

gray code to excess 3 code converter circuit and its logic diagram and ic based diagram

gray code to excess 3 code converter circuit and its logic diagram and ic based diagram

Solutions

Expert Solution

To convert gray code to Excess 3 code , we will first convert it to BCD and then convert it it excess 3 codes.

Lets say we have gray code with bits G1,G2,G3 and G4 ( G4 is LSB).

The equivalent binary would be A,B,C, D (D is LSB) and the equivalent excess 3 would be w,x,y,z (z is LSB).

We will need a 4 bit truth table to represent as there are 10 different BCD combinations possible.

We will use the following truth table to create the karnaugh maps for the conversion.

Decimal Value G1 G2 G3 G4 A B C D w x y z
0 0 0 0 0 0 0 0 0 0 0 1 1
1 0 0 0 1 0 0 0 1 0 1 0 0
2 0 0 1 1 0 0 1 0 0 1 0 1
3 0 0 1 0 0 0 1 1 0 1 1 0
4 0 1 1 0 0 1 0 0 0 1 1 1
5 0 1 1 1 0 1 0 1 1 0 0 0
6 0 1 0 1 0 1 1 0 1 0 0 1
7 0 1 0 0 0 1 1 1 1 0 1 0
8 1 1 0 0 1 0 0 0 1 0 1 1
9 1 1 0 1 1 0 0 1 1 1 0 0
10 1 1 1 1 X X X X X X X X
11 1 1 1 0 X X X X X X X X
12 1 0 1 0 X X X X X X X X
13 1 0 1 1 X X X X X X X X
14 1 0 0 1 X X X X X X X X
15 1 0 0 0 X X X X X X X X

Solving the Karnaugh Map -

The karnaugh Map for Gray Code to BCD Conversion is:

The karnaugh Map for BCD to Excess-3 code Conversion is:

Using the above Simplified Expressions, we can convert gray code to equivalent excess 3 code.

The simplified IC diagram representation is shown below:

Manojponduru answered 1 year ago
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