Codigo gray to bcd

DEPARTMENT OF MECHANICAL & AEROSPACE ENGINEERING UNIVERSITY AT BUFFALO
MAE 476/576 Mechatronics Spring 2003 Mini Assignment 4 – Solution

1. Design aGray 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 thedecimal numbers in binary form. The number representation requires 4 bits to store every decimal digit (from 0 to 9). Since there are 10 differentcombinations of BCD, we need at least a 4-bit Gray Code to create sufficient number of these combinations. The truth table is: Decimal 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 Gray Code B C 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 BCD D 0 1 1 0 0 1 1 0 0 1 1 0 0 1 10 W 0 0 0 0 0 0 0 0 1 1 D D D D D D X 0 0 0 0 1 1 1 1 0 0 D D D D D D Y 0 0 1 1 0 0 1 1 0 0 D D D D D D Z 0 1 0 1 0 1 0 1 0 1 D D D D D D

b. ApplyKarnaugh Map to look for the minimized logic expression. Karnaugh Map for W: A 00 0 0 0 0 01 0 0 0 0 B Minimal Expression for W: W=A Karnaugh Map for X: A 000 0 0 0 01 1 1 1 1 B Minimal Expression for X: X = A’B 11 0 0 D D 10 D D D D 11 1 1 D D 10 D D D D

C

00 01 11 10

D

C

00 01 11 10

DKarnaugh Map for Y: A 00 0 0 1 1 01 1 1 0 0 B Y = A’BC’ + B’C Karnaugh Map for Z: A 00 0 1 0 1 01 1 0 1 0 B 11 0 1 D D 10 D D D D 11 0 0 D D 10 D D D D

C00 01 11 10

D

C

00 01 11 10

D

Z = A’BC’D’ + B’C’D + AD + BCD + B’CD’

c. Implement the logic gates by using Circuit Maker.