Slide 1
Digital Logic Review
By Christopher Mar
NOT Gate
x
F
x F
NOT Gate
x
F
x F
0
NOT Gate
x
F
x F
0 1
NOT Gate
x
F
x F
0 1
1
NOT Gate
x
F
x F
0 1
1 0
AND Gate
x
F
x y F
y
AND Gate
x
F
x y F
0 0
y
AND Gate
x
F
x y F
0 0 0
y
AND Gate
x
F
x y F
0 0 0
0 1
y
AND Gate
x
F
x y F
0 0 0
0 1 0
y
AND Gate
x
F
x y F
0 0 0
0 1 0
1 0
y
AND Gate
x
F
x y F
0 0 0
0 1 0
1 0 0
y
AND Gate
x
F
x y F
0 0 0
0 1 0
1 0 0
1 1
y
AND Gate
x
F
x y F
0 0 0
0 1 0
1 0 0
1 1 1
y
Bitwise Operation
Perform logical operation between all inputs for each bit position
Bitwise AND Example
10011 AND 11001
10011
11001
1
0
0
0
1
AND
Lecture Question
What is the result of 01010 AND 10111?
10111
11111
10101
00010
01010
OR Gate
x
F
x y F
y
OR Gate
x
F
x y F
0 0
y
OR Gate
x
F
x y F
0 0 0
y
OR Gate
x
F
x y F
0 0 0
0 1
y
OR Gate
x
F
x y F
0 0 0
0 1 1
y
OR Gate
x
F
x y F
0 0 0
0 1 1
1 0
y
OR Gate
x
F
x y F
0 0 0
0 1 1
1 0 1
y
OR Gate
x
F
x y F
0 0 0
0 1 1
1 0 1
1 1
y
OR Gate
x
F
x y F
0 0 0
0 1 1
1 0 1
1 1 1
y
Lecture Question
What is the result of 01010 OR 10110?
10110
11111
11110
10110
01010
NOR (NOT OR) Gate
x
F
x y F
0 0 1
0 1 0
1 0 0
1 1 0
y
XOR (Exclusive OR) Gate
x y F
0 0 0
0 1 1
1 0 1
1 1 0
XOR Gate
x y F
0 0 0
0 1 1
1 0 1
1 1 0
XOR between any value and 1 inverts the value
Special Considerations for PLP
PLP ISA does not include an XOR or NOT
Boolean Algebra Properties
Annulment law
a & 0 = 0
a | 1 = 1
Identity law
a & 1 = a
a | 0 = a
Lecture Question
Which of the following would be equivalent to NOT $t5?
andi $t5, $t5, 0
andi $t5, $t5, 1
ori $t5, $t5, 0
ori $t5, $t5, 1
nor $t5, $t5, $t5
Multiplexer
i0
F
i1
s0
s0 i1 i0 F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1
s0 F
0 i0
1 i1
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