CSC 371 - Systems I: Computer Architecture and Organization

Dr. R. M. Siegfried

Assignment 3 - p.69-70/2-1, 2-2, 2-3, 2-8, 2-13, 2-17, 2-18

Due Monday, September 25, 2017

2-1

Demonstrate by means of a truth table the validity of the following identities:

1. DeMorgan's theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x' + y' + z'
2. The distributive law: x + yz = (x + y) (x + z)
3. The distributive law: x(y+z) = xy + xz
4. The associative law: x + (y + z) = (x + y) + z
5. The associative law: x(yz) = (xy)z

2-2

Simplify the following Boolean expressions to a minimum number of literals:

1. xy + xy'
2. (x + y) (x + y')
3. xyz + x'y + xyz'
4. (A + B)' (A' + B')'
5. (a + b + c)(a'b' + c)
6. a'bc + abc' + abc + a'bc'

2-3

Simplify the following Boolean expression to a minimum number of literals:

1. ABC + A'B + ABC'
2. x'yz + xz
3. (x + y)' (x' + y')
4. xy + x (wz + wz')
5. (BC' + A'D) (AB' + CD')
6. (a'+c')(a + b' + c')

2-8

Find the complement of F = wx + yz; then show that FF' = 0

2-13

1. y = [(u + x') (y' + z)]
2. y = (u ⊕ y)' + x
3. y = (u' + x') (y + z')
4. y = u(x ⊕z) + y'
5. y = u + yz + uxy)
6. y = u + x + x'(u + y')

2-17

Obtain the truth table of the following functions and express each function in sum of minterms and product of maxterms:

1. (b + cd)(c + bd)
2. (cd + b'c + bd')(b + d)
3. (c' + d) (b + c')
4. bd' + acd' + ab'c + a'c'

2-18

Given the Boolean function

1. Obtain the truth table of F.
2. Draw the logic diagram using the original Boolean expression
3. Use Boolean algebra to simplify the function to a minimum number of literals.
4. Obtain the truth table of the funciton from the simplified expression and show that it is the same as the one in part 1.
5. Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part 2.

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