Review for Chapter 4

All of the following should make sense when you understand the chapter
  1. BASES
    1. base 10 « binary 1210 = 11002
    2. hexadecimal « binary « octal 1316 = 000100112 = 0238
    3. hex ® base10 ß octal
  2. UNSIGNED NUMBERS *
    1. decimal « unsigned n bits
    2. greatest positive or smallest negative in n bits
    3. unsigned number <==> code ( if given the op table and register numbers - cf homework )
  3. 2's COMPLEMENT NUMBERS *
    1. decimal « 2's complement
      1. inverse
      2. greatest positive or smallest negative in n bits
    2. addition
      1. 'subtraction'
      2. overflow
    3. bit-wise AND
    4. bit-wise OR
    5. bit-wise NOT
  4. ALU
    1. adder circuit w/carry in, carry out
    2. signal tracing (e.g. given fig. 4.17 & inputs, find outputs)
    3. control inputs for +, -, AND, OR, NOT , slt
    4. overflow logic
  5. MULTIPLICATION *
    1. '3rd' algorithm
      1. product = [ 0…0 multiplicand ]
    2. Booth's algorithm
      1. product = [ 0…0 multiplicand 0 ]
      2. table: 00 ® X | 01® - | 10 ® + | 11 ® X (X means ' do nothing' )
      3. How may adds (sub = add) are done (saved) by Booth's algorithm?
    3. 3rd version of the multiply hardware (p 257)
  6. FLOATING POINT *
    1. IEEE 754 format ( other formats are possible with the same basic rules but different field lengths and biases)
      1. sign
      2. exponent
        1. bias
      3. mantissa
        1. normalization
          1. significand
    2. decimal fraction ç è IEEE 754 format (or other if given details)

* Note: in general I will probably not give 32-bit problems but rather 4, 8 or 16 bits problems for simplicity