EXAM #1 FOR LOGIC DESIGN                                       Fall 1996


NAME: ______________________________________

SSN: _______________________________________

CODE NAME: _________________________________ (optional)

Welcome to exam #1 for Logic Design.  You have exactly 75 minutes
to complete the seven required problems (each worth 14 points)
and the one extra credit problem (worth 7 points).  You may have
with you one 8.5 x 11 inch sheet of paper with anything on it.
Do not get bogged-down on any one problem, you will have to work
fast to complete this exam.  Be sure to show your work.  Good
luck and ask questions if you do not understand a problem.

PROBLEM #1:

Represent the following decimal numbers in sign-magnitude, 1's
complement, and 2's complement form.  Use only the necessary
number of bits.  Show all possible valid representations.

a) -12

b) 0

Convert the following hexadecimal number to Binary Coded Decimal.

c) 2A1

PROBLEM #2:

Give the following in canonical POS form.  Use any method(s) that
you wish to do the conversion.

  f(a,b,c,d) = a'bd + ad' + abc' + a'd'

PROBLEM #3:

Analyze the following circuit and redesign a minimized version
using only AND, OR, and NOT gates.  Remember that a "o" signifies
inversion.

          +------+      +------+
 A' ------+  AND +------+  XOR +o---- f
 B' ------+      |   +--+      |
          +------+   |  +------+
                     |
          +------+   |
 B' ------+   OR +---+
 C' ------+      |
          +------+

PROBLEM #4:

Minimize the following 5-variable function using any method(s)
that you wish.

  f(a,b,c,d,e) = Sum of m(0,1,12,16,17,24,25,28) + d(4,14,30)

PROBLEM #5:

A black box has four digital inputs (a, b, c, and d) and one
digital output.  The output should be zero only when input a is
"1" and exactly any two of inputs b, c, and d are "0".  Assume
that the input a = b = c = d = "0" can never occur.  Design a
two-level circuit with the least possible number of gates that
implements the black box function.  You can assume that you have
positive and negative inputs and that you have AND and OR gates
with up to 5 inputs.

PROBLEM #6:

Give a two-level static hazard-free AND-OR circuit that
implements the truth table for the following function.  Your
circuit should be minimized as much as possible.

  f(a,b,c,d) = a'b'c' + bc'd + abcd'

PROBLEM #7:

Minimize the following using the Quine-McClusky tabulation
method.  You must show your work.

  f(a,b,c,d) = Sum of m(0,1,4,5,6,11,14)

EXTRA-CREDIT PROBLEM:

Prove that NOR is functionally complete.