Chapter 9 Computer Arithmetic

1. Sign-magnitude Representation
   • Left most bit is sign bit.
   • 0 means positive
   • 1 means negative
   • Rarely used
2. Two's complement representation
   • 
   • Benefits
   • • One representation of zero
     • Arithmetic works easily
3. Conversion between lengths: left pack sign bit
4. Multiplication
   •                                                  
   • 
   • Multiplying negative numbers
   • • Solution 1
     • • Convert to positive if required
       • Multiply as above
       • If signs were different, negate the answer
     • Solution 2
     • • Booth's algorithm
       • • 
5. Division
   • 
   • Negative numbers division
   • • 
6. Floating point representation
   • Principle:  ±S*B ±E
   • • E: exponent, in computer, usually biased representation
     • • ±S*BE'
       • Typically, the bias = 2^(k-1) - 1. Exponent value = true exponent + bias
       • Thus, stored exponent value is unsigned.
7. Floating-point arithmetic
   • 
   • Add/Subtract
   • • Align significands(Adjusting exponents)
     • • Shifting the radix point on the smaller operand
       • Once the overflow occurs, the influence is smaller
     •