UK EE 280

= Design of Logic Circuts =

Theorems of Boolean Algebra

 * x = x
 * x+x = x
 * x*x = x
 * x+1=1
 * x*1=x
 * Absorption
 * x+xy=x
 * x(x+y)=x
 * Demorgan's
 * x+y = x * y
 * xy = x + y
 * Adjacency
 * xy+x y = x
 * (x+y)(x+ y ) = x
 * Consensus
 * xy + x z + yz = xy + x z
 * (x+y)( x +z)(y+z) = (x+y)( x +z)
 * x + x y = x+y
 * x*( x +y) = x*y

AND
a * b a | b | a*b 0 | 0 | 0 0 | 1 |  0 1 | 0 |  0 1 | 1 |  1

OR
a + b a | b | a+b 0 | 0 | 0 0 | 1 |  1 1 | 0 |  1 1 | 1 |  1

NOT
a a | a  0 | 1 1 | 0

NAND

 * AND NOT

F(a, b) = a*b = a + b a | b | a*b 0 | 0 | 1 0 | 1 |  1 1 | 0 |  1 1 | 1 |  0

NOR

 * OR NOT

F(a,b) = a + b = a * b a | b | a+b 0 | 0 | 1 0 | 1 |  0 1 | 0 |  0 1 | 1 |  0

XOR

 * Exclusive OR

F(a,b) = a b + a b a | b | a b + a b 0 | 0 | 0 0 | 1 | 1 1 | 0 |  1 1 | 1 |  0

XNOR

 * Exclusive NOR

F(a, b) = a * b = a + b

Verilog
Using Xilinx ISE 8.1.03i and ModelSim SE v6.1a


 * Family: Virtex2
 * Device: XC2V3000
 * Package: FF1152
 * Speed: -6


 * Sim: Modelsim
 * Check adv.