Chapter 5

1. 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

   

2. We start with a truth table showing when x is below y, F(x,y)

   x1	x0	y1	y0	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: