ECE2030A Fall 2008 Prof. H.-H. S. Lee
Georgia Tech Page 1 of 2
ECE2030A Introduction to Computer Engineering
Fall 2008
Homework Assignment #1
Assigned 09/08/08 Due in the first 5 min in class 09/15/08
No late turn-in accepted
1. (10%) Determine the numbers for all the question marks (?) shown in the following equations.
Note that all these numbers are “signed” numbers and are represented by two’s complement
using 2 bytes. Please show how you derive your answers step-by-step. You will not receive
any credit if you only write down your answers with no derivation.
1.1. (-183)10 = (?)16
1.2. (0125)7 = (?)9
1.3. (FFED)16 = (?)10
1.4. (0111 0010 0000 1110 1111 1010 0110 1100)2 = (?)16
1.5. (79)10 = (142)?
2. (20%) Gary tried to solve the equation 5x2 – 50x + 125 = 0 for his algebra homework
assignment. He came up with a solution x=5. All of a sudden, a flying saucer from Vega landed
in his backyard and a little green man coming out from the craft told him their solution of this
equation in fact is x=8 based on their number system. We (or Gray) use base-10 on earth, what
are the possible base(s) these outer space visitors use in their number system?
025150X5X2=+−
3. (20%) Draw CMOS circuits for the following two Boolean expressions. (You don’t need to
minimize the expression prior to your CMOS implementation. You only need to apply
DeMorgan’s Theorem and expand the XNOR function.)
C)DE()DBC A(F ++⋅⋅+⋅=
ACCEDBF ⋅+⊕⋅⋅=
4. (10%) (1) Minimize the following Boolean equations as much as possible. (Your minimized
equations should contain only “NOT”, “AND” and “OR” operators.) Please derive your new
expression using Boolean algebra only. (2) Then use Truth tables to verify the results of your
minimized equations.
4.1. B)(AA +⊕
4.2. B)(A BA ⋅⊕⊕
