Final Exam Review

Binary
  binary to decimal
  
      binary:       11010  
      power of two: 43210
      1 * 2^4 = 16
      1 * 2^3 = 8
      1 * 2^1 = 2
      
      16+8+2 = 26 (in decimal)
      
      decimal: 86
        keep dividing by two
        Quotient    Remainder
        86/2
        43/2        0
        21/2        1
        10/2        1
        5/2         0
        2/2         1
        1/2         0
        0           1
        Read binary from bottom up: 1010110
        
        1 * 2^1 = 2
        1 * 2^2 = 4
        1 * 2^4 = 16
        1 * 2^6 = 64
        = 86
       
  
  binary to hexadecimal
        AB3476 in hex
        A = 1010
        1010 1011 0011 0100 0111 0110
        
        0000  0
        0001  1
        0010  2
        0011  3
        0100  4
        0101  5
        0110  6
        0111  7
        1000  8
        1001  9
        1010  A
        1011  B
        1100  C
        1101  D
        1110  E
        1111  F
        
    Binary to Hex
        01 1011 -> 0001 1011 -> 1B
        
        0001 0011 -> 13
  
  
  hex, dec to ASCII : use the table!
  
  Circuit from a truth table:
  
    A B C  F
    0 0 0  1        1. Rows where F=1  (0,3,4)
    0 0 1  0        2. F is true when 0 OR 3 OR 4 are true
    0 1 0  0        3. Row 0 is true when NOT A AND NOT B AND NOT C
    0 1 1  1        4. Row 3 is true when NOT A AND B AND C
    1 0 0  1        5. Row 4 is true when A AND NOT B AND NOT C
    1 0 1  0       
    1 1 0  0
    1 1 1  0

F = (NOT A AND NOT B AND NOT C) OR (NOT A AND B AND C) OR (A AND NOT B AND NOT C)
    
    A B T
    0 0 1     T = NOT A AND NOT B
    0 1 0     T = NOT (A OR B)
    1 0 0     T = A NOR B
    1 1 0 
    
    
    A B   (A AND B)   R=(A NAND B)
    0 0     0           1
    0 1     0           1
    1 0     0           1
    1 1     1           0
    
    R = A NAND B
    R = NOT(A AND B)
    R = (NOT A AND NOT B) OR (NOT A AND B) OR (A AND NOT B)