D511133160 — Digital Logic Design — Homework 1.
Due March 19th 12:00, 2025
Unit 1 Introduction Number Systems and Conversion
Unit 2 Boolean Algebra
Unit 3 Boolean Algebra (Continued)
1.
(20%)
(a) A = 101010 and B = 011101 are 1’s complement numbers. Perform the following operations
and indicate whether overflow occurs.
(i) A + B
(ii) A − B
(b) Repeat part (a) assuming the numbers are 2’s complement numbers.
2.
(30%) Simplify the following expressions to a minimum sum of products.
(a) [(AB)′ + C′D]′
(b) [A + B(C′ + D)]′
(c) ((A + B′)C)′(A + B)(C + A)′
3.
(20%) Draw a circuit that uses two OR gates and two AND gates to realize the following
function:
F = (V + W + X)(V + X + Y)(V + Z)
4.
(30%) Eliminate the exclusive OR, and then factor to obtain a minimum product of sums:
(a) (KL ⊕ M) + M ′N ′
(b) M ′(K ⊕N ′) + MN + K ′N