Chapter 7

Switches - transistors

Logical functions: and, or, not

NOT

  A   NOT A = A'
  0   1
  1   0
  
  0 = false
  1 = true
  
 AND
 
  A B   A and B = AB
  0 0   0
  0 1   0
  1 0   0
  1 1   1
  
 OR
  A B   A or B = A+B
  0 0   0
  0 1   1
  1 0   1
  1 1   1
  
  Gate: simple digital device that
  performs a logical function
  
 NAND
  A B   A nand B = (AB)'
  0 0   1 
  0 1   1
  1 0   1
  1 1   0
 
 (see 4-15_fig1.png)
 Function?
  A B   F
  0 0   1
  0 1   1
  1 0   0
  1 1   0
  
  F = A'B' + A'B
  
  Lab 7.2...
  
  XOR
 A  B   A xor B
 0  0     0
 0  1     1   <--- row 1
 1  0     1   <--- row 2
 1  1     0
 
 Convert truth table to function
 1. Find rows where the function
    is one.
    
 2. Make a function that is true
    when row 1 is true or row 2
    is true:
    F = row1 + row2
  
 3. What makes row 1 true?
    A=0 and B=1
    A=0 when A' is true
    row 1 is true when A'B is true
 
 4. What makes row 2 true?
    A=1 and B=0
    B=0 when B' is true
    row 2 is true when AB' is true.
 
 so F = A'B + AB'
 see 4-15_fig2.png
  
  
A B C   G
0 0 0   0
0 0 1   0
0 1 0   1  <---  A'BC'
0 1 1   1  <---  A'BC
1 0 0   0
1 0 1   1  <---  AB'C
1 1 0   1  <---  ABC'
1 1 1   0

G = A'BC' + A'BC + AB'C + ABC'