l 04 logic gates

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Boolean Algebra (Binary Logic) {0, 1} 0: Low 0.0 Volt 1: High 5.0 Volt

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logic gates

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Page 1: l 04 Logic Gates

Boolean Algebra (Binary Logic)

{0, 1}

0:    Low 0.0 Volt

1:    High 5.0 Volt

Page 2: l 04 Logic Gates

Boolean Algebra (Binary Logic)

{0, 1}

0:    Low 0.0 Volt False OFF

1:    High 5.0 Volt True ON

Page 3: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR

Page 4: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR 0+0=0        0+1=1 1+0=1 1+1=1

Page 5: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR 0+0=0        0+1=1 1+0=1 1+1=1

*    :    AND

Page 6: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR 0+0=0        0+1=1 1+0=1 1+1=1

*    :    AND 0*0=0        0*1=0 1*0=0 1*1=1

Page 7: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR 0+0=0        0+1=1 1+0=1 1+1=1

*    :    AND 0*0=0        0*1=0 1*0=0 1*1=1

’    :    NOT 0’=1        1’=0

Page 8: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Operation

+    :    OR

*    :    AND

’    :    NOT

Page 9: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

+    :    OR

Page 10: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

+    :    OR

Timing

Page 11: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Timing

I t B

Input A

Input B

Output

Page 12: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

*    :    AND

Page 13: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

*    :    AND

Timing

Page 14: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Timing

I t B

Input A

Input B

Output

Page 15: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

’    :    NOT

Page 16: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Circuit

’    :    NOTTiming

Page 17: l 04 Logic Gates

Boolean Algebra (Binary Logic)

Timing

Input

O t tOutput

TpNOT

Input

Output

0 ns10 ns

Page 18: l 04 Logic Gates
Page 19: l 04 Logic Gates

X

Y

X = a * b = ab

Y = c * d = cd

z = X + Y = ab + cd

Page 20: l 04 Logic Gates

X

s’

Y

X = a * s’ = as’

Y = b * s = bs

z = X + Y = as’ + bs

Page 21: l 04 Logic Gates
Page 22: l 04 Logic Gates