2. How many additions and multiplications are required to evaluate the polynomia

Question

2. How many additions and multiplications are required to evaluate the polynomial Q(x) = 5x6-25x' + 15 in nested form by thinking of a) Q(x) as a polynomial in x b) Q(x) as a polynomial in x3 Convert the base 10 numbers to binary and express as a binary floating point number fi(x) by using Rounding to Nearest Rule (but not as the machine represented number) a) 20.375 3. b) -6.1 Do the following sums using IEEE Rounding to Nearest Rule. Express as a binary floating point number fl(x) a) (2+(24.51+24-53+24-54)-2 4. b) (2+(2A-51+2A-52))-2

Explanation / Answer

Question 2 .

(a) Q(X) = 5x6 - 25 x3 + 15

in nested form when written in the form of polynomial of x

Q(x) = 5 * x * x * x * x* x* x - 25 * x * x * x + 15

so total 11 additions and multiplications

if written in form of polynomial of x3

in nested form

Q(X) = 5 * x3 * x3 - 25 * x3 + 15

so 5 additiona and multiplications.

Q.3 (a)

(20.375)10 in binary number

20 = 4 + 20 so in binary it is 10100

for 0.375

it would be multplied by 2 => 0.75 gives 0

0.75 * 2 => 1.5 gives 1 left 0.5

0.5 * 2=> 1 gives 1 left nothing

so 20.375 = 10100.011

(b) -6.1 =?

-6 = -110 (as 2 + 4)

for 0.1 it would given

0.1 x 2 = 0.2 gives 0 and leaves 0.2

0.2 x 2 = 0.4 gives 0 and leaves 0.4

0.4 x 2 = 0.8 gives 0 and leaves 0.8

0.8 x 2 = 1.6 gives 1 and leaves 0.6

0.6 x 2 = 1.2 gives 1 and leaves 0.2

so same process will repeat

so .1 = 0.00011001100110011

so -6.1 = -110.00011001100110011

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