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日期:2021-03-07 10:58

CISC 260 Machine Organization and Assembly Language

(Spring 2021)

Assignment # 2

(Due: March 10, 2021)

1. [25 points] Given the following truth table, where X, Y, and Z are input and W is

output, write the canonical expression and generate gate-level logical circuit

(draw the wire diagram).

X Y Z W

0 0 0 1

0 0 1 1

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 0

1 1 0 1

1 1 1 1

2. [25 points] Simply the following Boolean expressions as much as you can.

a) Y= BC + ~A~B~C + B~C

b) Y = ~(A+~AB+~A~B) + ~(A+~B)

3. [25 points] You are asked to design a circuit to detect if an overflow occurs when

adding two integers represented in two's complement: Z = X + Y. Let Sz, Sx, and

Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the

circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow

happens, and 0 if otherwise.

a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz.

b) Write the canonical expression (sum-of-product) for the Boolean function

defined in the part a.

c) Implement the Boolean expression defined in part b with a circuit by using

AND, OR, and NOT gates. Draw the wiring diagram.

4. [25 points] Prove that NOR gate is universal, by showing how AND, OR, and NOT

gates can be built by wiring a bunch of NOR gates. Draw the wire diagram for each

case.


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