Transcript Slide 1
Review for Exam 1
Conversion from one number base to another
Binary arithmetic
Equation simplification
DeMorgan’s Laws
Conversion to/from SOP/POS
Reading equations from Truth Tables
Boolean expression to Karnaugh Map
Minimization using Karnaugh Maps
Minterm and Maxterm Equations
Minimization using don’t cares
Logic to Boolean Expression conversion
Word problems
Determining how many gates and inputs a boolean expression has
Determining Prime Implicants and Essential Prime Implicants
Logical completeness
Conversion from one number base to another
356.8910 to Hexadecimal (2 digits)
Conversion from one number base to another
Binary arithmetic
23
6 | 141
-12
21
-18
3
Equation simplification
Y = (AB’ + (AB + B)) B + A
Simplify and convert to SOP
(A’ + B + C’)(A’ + C’ + D)(B’ + D’)
Equation simplification
X + XY = X
X + X’Y = X + Y
X + XY = X
(X + Y)(X + Z) = (X + YZ)
DeMorgan’s Laws
G = {[(R + S + T)’ PT(R + S)’]’T}’
DeMorgan’s Laws
G = {[(R + S + T)’ PT(R + S)’]’T}’
= [(R + S + T)’ PT(R + S)’] + T’
= [ R’S’T’ PT(R’S’)] + T’
= R’S’T’PTR’S’ + T’
= R’S’P(T’T) + T’
= T’
Conversion to/from SOP/POS
(X + YZ) = (X + Y)(X + Z)
Reading equations from Truth Tables
A
B
C
D
F
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
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1
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0
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0
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1
1
1
1
0
0
0
0
1
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0
1
0
1
0
1
0
0
1
0
1
1
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1
1
0
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1
1
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1
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1
1
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1
1
0
Reading equations from Truth Tables
A
B
C
D
F
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
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0
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0
0
1
1
0
1
A’BCD’
0
1
1
1
1
A’BCD
1
0
0
0
0
1
0
0
1
0
1
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1
0
0
1
0
1
1
0
1
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1
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0
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0
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1
1
0
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1
1
1
1
0
A’B’C’D’
A’BC’D’
ABC’D’
ABCD’
Boolean expression to Karnaugh Map
AB + C’D + A’B’C + ABCD + AB’C
AB
CD
00
00
01
11
10
01
11
10
Boolean expression to Karnaugh Map
AB + C’D + A’B’C + ABCD + AB’C
AB
CD
00
01
00
11
10
1
01
1
11
10
1
1
1
1
1
1
1
1
1
Minimization using Karnaugh Maps
AB
CD
00
AB + C’D + A’B’C + ABCD + AB’C
01
00
11
10
1
01
1
11
10
1
1
1
1
1
1
1
1
1
AB + C’D + B’C
Minterm and Maxterm Equations
F(ABCD) = Sm (0,2,4,7,9,12,14,15)
AB
CD
00
01
11
10
00
01
11
10
BC’D’ + BCD + ABC + A’B’D’ + AB’C’D
Minterm and Maxterm Equations
F(ABCD) = Sm (0,2,4,7,9,12,14,15)
AB
CD
00
00
01
11
1
1
1
01
1
11
10
10
1
1
1
1
BC’D’ + BCD + ABC + A’B’D’ + AB’C’D
Minimization using don’t cares
F(ABCD) = Sm (0,1,2,11,13) + Sd (3,9,12,15)
AB
CD
00
01
00
01
11
10
A’B’ + AD
11
10
Minimization using don’t cares
F(ABCD) = Sm (0,1,2,11,13) + Sd (3,9,12,15)
AB
CD
00
01
11
10
00
1
x
01
1
1
x
11
x
x
1
10
1
A’B’ + AD
Logic to Boolean Expression conversion
Logic to Boolean Expression conversion
F = (XY + W)Z + V
F = (B+C)A + BC
Word problems
Determining how many gates and inputs a boolean expression has
F = (XY + W)Z + V
levels
gates
inputs
transistors
inputs/gate max
Z = A’B’C’ + ABC + BCD +B’C’D’
levels
gates
inputs
transistors
inputs/gate max
Determining how many gates and inputs a boolean expression has
F = (XY + W)Z + V
4 levels
4 gates
8 inputs
16 transistors
2 inputs/gate max
Z = A’B’C’ + ABC + BCD +B’C’D’
2 levels
5 gates
16 inputs
32 transistors
4 inputs/gate max
Determining Prime Implicants and Essential Prime Implicants
AB
CD
00
01
00
1
1
01
1
1
11
x
10
1
11
10
1
1
x
x
1
Determining Prime Implicants and Essential Prime Implicants
6 prime implicants
AB
CD
00
01
00
1
1
01
1
1
11
x
10
1
11
10
1
1
x
x
1
3 essential prime
implicants
Logical completeness
Inverter
AND gate
OR gate
Logical completeness
Inverter
Inverter
AND gate
NAND
Inverter
Inverter
NAND gate
OR gate