1. Design a Gray Code to BCD converter by the following ...
DEPARTMENT OF MECHANICAL & AEROSPACE ENGINEERING UNIVERSITY AT BUFFALO
MAE 476/576 Mechatronics Spring 2003
Mini Assignment 4 ? Solution
1. Design a Gray Code to BCD converter by the following procedures: a. Write down the truth table of the converter.
Binary Coded Decimal (BCD) is a way to store the decimal numbers in binary form. The number representation requires 4 bits to store every decimal digit (from 0 to 9). Since there are 10 different combinations of BCD, we need at least a 4-bit Gray Code to create sufficient number of these combinations.
The truth table is:
Decimal A
Gray Code
B
C
D
W
BCD
X
Y
Z
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
1
1
4
0
1
1
0
0
1
0
0
5
0
1
1
1
0
1
0
1
6
0
1
0
1
0
1
1
0
7
0
1
0
0
0
1
1
1
8
1
1
0
0
1
0
0
0
9
1
1
0
1
1
0
0
1
10
1
1
1
1
D
D
D
D
11
1
1
1
0
D
D
D
D
12
1
0
1
0
D
D
D
D
13
1
0
1
1
D
D
D
D
14
1
0
0
1
D
D
D
D
15
1
0
0
0
D
D
D
D
b. Apply Karnaugh Map to look for the minimized logic expression.
Karnaugh Map for W: A
00 01 11 10
00 0 0 1 D
C
01 0 0 1 D 11 0 0 D D 10 0 0 D D
D
B
Minimal Expression for W: W = A
Karnaugh Map for X: A
00 01 11 10
00 0 1 0 D
C
01 0 1 0 D 11 0 1 D D 10 0 1 D D
D
B
Minimal Expression for X: X = A'B
Karnaugh Map for Y:
A
00 01 11 10
00 0 1 0 D
C
01 0 1 0 D 11 1 0 D D 10 1 0 D D
D
B
Y = A'BC' + B'C
Karnaugh Map for Z: A
00 01 11 10
00 0 1 0 D
C
01 1 0 1 D 11 0 1 D D 10 1 0 D D
D
B
Z = A'BC'D' + B'C'D + AD + BCD + B'CD'
c. Implement the logic gates by using Circuit Maker.
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