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Transcript 
Truth Table of a Boolean Function
Circuit
* : AND
Truth Table of a Boolean Function
a b c f
3-input AND function
a
b
c
f
0
1
2
3
4
5
6
7
0 0 0 0
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 1
Truth Table of a Boolean Function
a b c f
3-input AND function
a
b
c
f
f = a*b*c
0
1
2
3
4
5
6
7
0 0 0 0
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 1
Converting truth table
to Boolean equation
a b c d z
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Converting truth table
to Boolean equation
a b c d z
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Converting truth table
to Boolean equation
a b c d z
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
z = a’b’cd
+ a’bcd
+ ab’cd
+ abc’d’
+ abc’d
+ abcd’
+ abcd
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Converting truth table
to Boolean equation
a b c d z
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
z = a’b’cd
+ a’bcd
+ ab’cd
+ abc’d’
+ abc’d
+ abcd’
+ abcd
= ab + cd
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Converting truth table
to Boolean equation
a b c d z
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
z = ab + cd
0 0 1 1 1
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Converting Boolean
Equation to truth table
X
X = ab
Y = cd
Y
z = X + Y = ab + cd
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
Y
z
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
0
0
0
0
0
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
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
X
Y
z
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
Y
z
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
Y
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
z
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
Y
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
z
Converting Boolean
Equation to truth table
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
Y
z
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
X
Y
X = ab
Y = cd
z = X + Y = ab + cd
a
b
c
d
X
Y
z
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
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