Question

BCD decrement

(Two Level Combinational Circuit Design) – A BCD decrementer is very similar to the BCD incrementer discussed in class. The function of this circuit is to decrementthe input BCD number by two. The outputs are ”don’t care” if the input is not a BCD digit and the output of the decrementer given the input of 0000 is 1001.

a. Complete the truth table for the BCD decrementer.

Example BCD decrement by two

A B C D W X Y Z
0 0 0 0 1 0 0 1
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0 X X X X
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

b. Represent the output functions W and X in sum of products form using little m notation.

c. Use the provided Karnaugh maps to find a minimized sum of products form for W and X.

d. Draw the schematic for the BCD decrementer output functions W and X.

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