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
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) = (
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