Boolean logic in CMOS
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University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell Boolean logic in CMOS
Transcript of Boolean logic in CMOS
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell
Boolean logic in CMOS
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 2
Representations of Boolean logic
Truth tableBoolean equationCircuit element (gate)
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 3
Truth table
Brute force I/O specificationGrows exponentially with number of inputs
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 4
Boolean algebra
Identitiesx + 0 = xx + 1 = 1x + x = xx + x’ = 1x’’ = xx * 1 = xx * 0 = 0x * x = xx * x’ = 0
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 5
Boolean algebra
Commutativityx + y = y + xx * y = y * xAssociativityx + (y + z) = (x + y) + zx * (y * z) = (x * y) * z
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 6
Boolean algebra
Distributivex * (y + z) = x*y + x*zx + (y * z) = (x+y) * (x+z)
= x + xy + xz + yz= x(1+y) + xz + yz= x + xz + yz= x(1+z) + yz= x + yz
De Morgan(x + y)' = x' * y'(x * y)' = x' + y'
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 7
CMOS gates - NOT
gnd0110
OutIn
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 8
CMOS gates - NAND
gnd
a
b
Vdd
011101
10B
1010
OutA
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 9
CMOS gates - NOR
a
b
Vdd
011001
10B
0010
OutA
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 10
CMOS gates - AND
NO!Logically correct, butviolates n to n and p to p rule,passes weak values
111001
10B
0000
OutAVdd
A
B Out
Vdd
A
B
Out
University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 11
CMOS gates - OR
A
B Out
Vdd
111101
10B
1000
OutA
