CS 224, Su2016
Homework #2
S02: Digital Logic
Name
Questions:
A = 0101 0110
B = 0111 0000
NOT A
A OR B
A AND B
A NOR B
A NAND B
A XOR B
A AND B OR NOT A
2. (8 points) Using the A and B values above as
2’s complement numbers, compute the
following 8-bit arithmetic operations :
a.
b.
c.
d.
Please initial to permit
public return (FERPA)
Score
/71
Answers:
1. (7 points) Compute the following bitwise
logical operations given the values of A and B?
a.
b.
c.
d.
e.
f.
g.
Section
NEG A
A ADD B
A SUB B
A SUB B ADD NEG B
a.
b.
c.
d.
e.
f.
g.
a.
b.
c.
d.
3. (8 points) Program the following equation
into the Programmable Logic Array (PLA) to
the right by filling in (marking) the appropriate
question mark boxes to make wire connections.
(The  symbol is an exclusive OR, left to right
associativity.)
Z=ABC
4. (9 points) A milling machine has two
switches, either one will turn the machine
on/off. (The machine will not operate with both
switches on.) Switch S1 is on the side of the
machine and switch S2 is on the floor. In
addition, the machine has two cut-off microswitches, switch M1 is on a guard surrounding
the milling tool and the second switch M2 is on
the access door to the internal mechanism of
the milling machine. For
safety reasons, both microswitches must be closed
(logic ‘1’) before the machine
can operate.
Using AND’s, OR’s, and
NOT’s, a) write an equation
and b) draw a logic circuit for
this machine.
BYU, CS 224, Su2016
Homework #2
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5. (10 points) Complete the timing relationship
for the following master-slave flip-flop.
(Assume the flip-flop is in the clear state prior
to the occurrence of the clock pulse.)
C
D
Y
Y
Q
Q'
6. (9 points) Fill in the blank entries of the state
table to the right for the state diagram below.
The Boolean value below the state names 0¢,
5¢, 10¢, and 15¢ is the current output Z.
Next State
Current
State
Output
Z
N
0¢
0
5¢
D
5¢
10¢
15¢
7. Consider the following simple microwave
controls:
10¢
a. State Diagram:
TEMP, START/STOP, and RESET are buttons
whose input values are 0 (normal) and 1
(pressed).  and  are output display lights
that are either on (1) and off (0).
The TEMP button cycles from no temperature
setting ( and  off), to low temperature (
on  off), to high temperature ( off  on),
and then toggles between high and low
thereafter (if not running).
The START/STOP button turns the microwave
on and off (if a temperature has been selected.)
The RESET turns the microwave off and clears
any temperature setting.
a. (10 points) Using the symbols T for TEMP, S
for START/STOP, and R for RESET, create a
finite state diagram for the operation of the
microwave. (Ignore impossible states and
simultaneous pressing of buttons.)
b. (10 points) Using the above symbols plus
“s3” for microware off/on, “s2” for  off/on,
and “s1” for  off/on, fill in the truth table of
the finite state machine for the operation of the
microwave (5 states, 4 actions/rows per state).
BYU, CS 224, Su2016
b. Truth Table:
T
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
Input
S
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
R
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
Homework #2
Current State
s3
s2
s1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
Next State
s3' s2' s1'
0
0
0
0
0
0
0
0
1
Behavior of
Current State
Idle
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