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ENSC252, Fall 2024

Practice Questions #2

1. (10marks) Simplify the following functions, F, together with the don’t-care conditions d, and then express the simplified function in sum of minterms:

a) F(A, B, C, D) = Σ (0, 6, 8, 13, 14) +  d(2, 4, 10)

b) F(A, B, C, D) = Σ (1,3,5,7,9,15) + d(4,6,12,13)

2. (10 marks) Simplify the following expressions using K map, and implement them with NAND gate circuits:

a) AB ’ + ABD + ABD ’ + A’C’D ’ + A’BC ’

b) BD + BCD ’ + AB’C’D ’

3. (10 marks) Implement half adder circuit using only NAND gates.

4. (15marks) Construct a half subtractor circuit which performs subtraction of the two inputs A and B and Outputs are B(borrow) and D(difference).

5. (20 marks) Using 8 bit 2’s complement numbers, perform the following.

a)104 +22    b) 125- 45     c) – 98 - 21    d) -65-47

6. (20) Using half subtractor, implement full subtractor circuit whose inputs are X, Y, bin  and outputs are B(Borrow) and D(difference).

7. (15 marks) Find the minimum cost POS form for the function

f (A, B,C, D,E) = πM (1, 4, 6, 7, 9, 12,15, 17, 20,21,22, 23,28, 31)