1. Boolean logic in CMOS

2. Representations of Boolean logic
Truth table
Boolean equation
Circuit element (gate)
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3. Truth table Brute force I/O specification
Grows exponentially with number of inputs
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4. Boolean algebra Identities x + 0 = x x + 1 = 1 x + x = x x + x’ = 1
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5. Boolean algebra Commutativity x + y = y + x x * y = y * x
Associativity
x + (y + z) = (x + y) + z
x * (y * z) = (x * y) * z
University of Texas at Austin CS Computer Organization Spring Don Fussell

6. Boolean algebra Distributive x * (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 CS Computer Organization Spring Don Fussell

7. CMOS gates - NOT In Out 1 gnd1
University of Texas at Austin CS Computer Organization Spring Don Fussell

8. CMOS gates - NAND A B Out 1 gnd Vdd a b1
gnd a b
Vdd
University of Texas at Austin CS Computer Organization Spring Don Fussell

9. CMOS gates - NOR A B Out 1 Vdd a b1
University of Texas at Austin CS Computer Organization Spring Don Fussell

10. CMOS gates - AND A B Out 1 NO! Logically correct, but
Vdd A B
Out
Vdd A B
Out A B
Out 1
NO!
Logically correct, but
violates n to n and p to p rule,
passes weak values
University of Texas at Austin CS Computer Organization Spring Don Fussell

11. CMOS gates - OR A B Out 1 Vdd A Out B1
University of Texas at Austin CS Computer Organization Spring Don Fussell