Design & Implementation of a
Four-Bit Binary to Gray Code Encoder
Objective
To design a combinational circuit with four inputs and four outputs that converts a four-bit binary number into its equivalent four-bit gray code number. Implement the circuit using exclusive-OR gates.
Input/Outputs
Four one-bit inputs (Bin3 (MSB), Bin2, Bin1, Bin0 (LSB))
Four one-bit outputs (Gray3 (MSB), Gray2, Gray1, Gray0 (LSB))
Truth Table
INPUTS |
OUTPUTS |
||||||
Bin3 |
Bin2 |
Bin1 |
Bin0 |
Gray3 |
Gray2 |
Gray1 |
Gray0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
Karnaugh Maps
Gray3 |
|||||
Bin1 Bin0 |
Bin3 Bin2 |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 0 |
1 |
1 |
|||
0 1 |
1 |
1 |
|||
1 1 |
1 |
1 |
|||
1 0 |
1 |
1 |
|||
Gray 3 = Bin3
Gray2 |
|||||
Bin1 Bin0 |
Bin3 Bin2 |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 0 |
1 |
1 |
|||
0 1 |
1 |
1 |
|||
1 1 |
1 |
1 |
|||
1 0 |
1 |
1 |
|||
Gray2 = Bin2’ . Bin3 + Bin2 . Bin3’
= Bin2
Å Bin3
Gray1 |
|||||
Bin1 Bin0 |
Bin3 Bin2 |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 0 |
1 |
1 |
|||
0 1 |
1 |
1 |
|||
1 1 |
1 |
1 |
|||
1 0 |
1 |
1 |
|||
Gray1 = Bin1’ . Bin2 + Bin1 . Bin2’
= Bin1
Å Bin2
Gray0 |
|||||
Bin1 Bin0 |
Bin3 Bin2 |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 0 |
|||||
0 1 |
1 |
1 |
1 |
1 |
|
1 1 |
|||||
1 0 |
1 |
1 |
1 |
1 |
|
Gray0 = Bin0’ . Bin1 + Bin0 . Bin1’
= Bin0
Å Bin1
Circuit Implementation