Joshua Brooks
Cs210
Homework #2
2.1: Prove the following theorems algebraically:
a. X(X+Y)=XY= XX+XY=0+XY=XY
b. X+XY=X = X(1+Y)=X(1)=X
c. XY+XY=X = X(Y+Y)=X(1)=X
d. (A+B)(A+B)=A
= AA+AB+BA+BB =A(1+B+B)=2A=A
2.3: Simplify each of the following expressions
Loop an essential prime implieant! [Hit Enter]
[Hit F12 when finished]
AB
on
01 11 1o
[II]
[ll
11
1|]
F = [mo]
Loop a remaining term for minimum solution! [Hit Enter]
[Hit F12 when finished]
A B
c D oo 01 11 10
oo 11 DJ i
CS210 Computer Logic
Chapter 1: Digital computers and information
Information representation:
1. A bit (o or 1) is represented by a voltage value rage. For example,
from 4.0 to 5.0 volts for 1 and from 0.0 to 1.0 volts for 0.
2. The two voltage ranges mus
CS 210 Computer Logic
Winter 2002
Test#2
1. (10 points) Use D-flip-flops to design a counter that counts the following sequence:
000
001
100
011
110
111
101
000
Show all your work, transition table and simplified equations, and then draw the circuit.
2. (
Department of Computer Science
Course Description
Summer 2012
Course Number and Title
CS210 Computer Logic
Instructor
Dr. Salam Salloum
Office: Bldg. 8 Room 13
Office Hours: TTH 4:00-5:00PM, W 1:00-3:00PM, and by appointment.
Phone: (909) 869-5317
E-mail:
Chapters 2-5 & 7 Combination Logic Circuits
Binary Variables and Operators
1. A variable is called binary variable(or Boolean variable) if it takes on two
discrete values: 0 and 1.
2. The basic operators associated with binary variables are:
(a) AND: This
Chapter 4 Arithmetic
PART 1.
Binary Adder and Subtracter
1. Full adder is a circuit that performs the addition of three inputs X, Y, and Z; and
generates the sum bit S and the carry bit C. The following table shows the truth
table of this circuit.
XYZ
000
Joshua Brooks
CS210
Homework#4
4.9:
A: F(a,c,b)=abc+b = abc+b(c+c)(a+a) = abc+abc+abc+abc+abc = F=m(0,1,4,5,6)
B: The terms that are not min are max so F=M(2,3,7)
4.10:
F(a,b,c,d) =(a+b+d)(a+c)(a+b+c)(a+b+c+d) = (00X0)(1XX0)(111X)(0011) so M =
0000,0010,1
Joshua Brooks
CS210
Homework #3
2.4:
A. F=(A1)+(A1)+E+BCD = (A+A)+E+BCD
=
A+E+BCD
NOTE: Circuit is on separate sheet
B. Y=(AB+(AB+B)B+A = (AB+B)B+A = (A+B)B+A = AB+B+A = B(A+1)+A =A+B
NOTE: Circuit is on separate sheet
2.9:
A: F=(A+B)+(A+(A+B)(A+(A+B) = (
Joshua Brooks
CS210
Homework #3
2.4:
A. F=(A1)+(A1)+E+BCD = (A+A)+E+BCD = A+E+BCD
NOTE: Circuit is on separate sheet
B. Y=(AB+(AB+B)B+A = (AB+B)B+A = (A+B)B+A = AB+B+A = B(A+1)+A =A+B
NOTE: Circuit is on separate sheet
2.9:
A: F=(A+B)+(A+(A+B)(A+(A+B) = (