EECS 284 Winter 2000

Homework 2 Solutions

Problem 1

a)  
IN1
IN2
IN3
  
OUT
0
0
0
  
1
0
0
1
  
0
0
1
0
  
0
0
1
1
  
0
1
0
0
  
0
1
0
1
  
0
1
1
0
  
0
1
1
1
  
0
  b)
  Problem 2 a) With a two-input function there can be a total of 22 = 4 outputs. So the total number of different functions possible is 24, or 16.

b)

c)

Problem 3

a) There are be a total of 26 = 64 outputs.

b)

c) A multiplexer with 27 different input lines will need 5 select line since 24 = 16 < 27 < 25 = 32.

Problem 4
a)
 
A
B
C
0 0 0
0 1 0
1 0 1
1 1 0
 
b)
c)  Since the set of gates {AND, NOT} is logically complete, we can prove that the set {NEWOP, NOT} is logicaly complete if we show that we can construct circuits that are logically equivalent to AND and NOT, using only gates from the set {NEWOP, NOT}.  The NOT, of course, is taken care of by the NOT in {NEWOP, NOT}.  We can construct a circuit that is logically equivalent to AND, as follows:  A AND B is equivalent to A NEWOP NOT B:
 
Problem 5
A
B
C
Z
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0

Problem 6

a) The total number of D-latches that would be used to construct such a memory is 216 * 24 = 1572864
b) The address space is number of uniquely addressable location = 216 = 65536