EEL2020 Digital Design
Assignment 01 Review of Number systems and Combinational Logic Circuits
Number System Conversion
1.
Convert the following numbers into various number systems (Show the steps of the
interconversion.)
(a) (100)10 = ( ? )2 = ( ? )8 = ( ? )16
(b) (25AF)16 = ( ? )2 = ( ? )8 = ( ? )10
(c) (370)8 = ( ? )2 = ( ? )10 = ( ? )16
2.
Write the following numbers in words: (Eg. (27)10 is Twenty-seven to the base 10)
(ii) (100)2
(iii) (670)8
(i) (100)10
Review of Combinational Circuits and Minimization
3.
Given the following Boolean function: F = A’C + A’B + AB’C + BC,
(a) express it in sum of minterms;
(b) find the minimal boolean expression using K-Map; and
(c) represent the minimized function using logic gates.
4.
Simplify the Boolean function: F(w, x, y, z) = Σ(0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14) using KMap.
5.
Design a combinational circuit with three inputs, x, y, and z, and three outputs, A, B,
and C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the
input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the
input.