Answer to Quiz 2 Fri 21 Jan 2005

Consider the evaluation of polynomials.
1. Let p = a0 + a1*x + a2*x^2 + a3*x^3.
  How many additions and multiplications are needed to evaluate p?
  Answer:
```
    number of additions : 3 ( just count the plus signs )
    number of multiplications : 1 + 2 + 3 = 6

    Storing x^2 as y brings the number of multiplications
    down to 5.
```
2. Let q = ((a3*x + a2)*x + a1)*x + a0.
  How many additions and multiplications are needed to evaluate q?
  Answer:
```
    number of additions : 3
    number of multiplications : 3
```

Assume the floating-point arithmetic on our computer has base 10, with 4 decimal places in the fraction (or mantissa), and exponents ranging between -10 and +10.
Show the evaluation of 34.42 + 0.012 in this floating-point system.

Answer:

  represent:
              34.41 = +.3441 10^2
              0.012 = +.1200 10^(-1)
  align:
                    = +.0001200 10^2
  add:
            +.3441    10^2
            +.0001200 10^2
            --------------
            +.3442200 10^2

  round:
            +.3442 10^2 = 34.42