CISC 260 Machine

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
2. 0 0 1
3. 0 1 1
4. 1 0 0
5. 1 1 0
6. 0 0 0
7. 0 1 0
8. 1 0 1
9. 1 1 1
10. [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)
11. [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.
12. [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.