Chapter 5
 Using NOR gates.

Using truth tables
x x ¬(x ∨ x) 0
0
1
1
1
0
we can design a NOT gate,

an AND gate,
x y ¬x ¬y ¬(¬x ∨ ¬x) 0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1

and an OR gate
x y ¬(x ∨ x) ¬(¬(x ∨ x)) 0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1


We start with a truth table showing when x is below y, F(x,y)
x_{1} x_{0} y_{1} y_{0} F(x,y) 0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
F(x,y) can be implemented with NAND gates: