floating point exam questions

1a) In binary, write in the boxes below, the smallest positive number that can be represented using this normalized floating point system.

0.0000001 0001

b) calculate the denary equivalent of the number.
1.0110000 0010

exponent = 0010 = 2
101.1000 = -4 + 1 + 0.5 = -2.5

c) write the normalised floating point representation of the denary value 12.75.

01100.11
0.110011 = 4

0.110011 0100

d) state two advantages of using a normalised representation

1. Simplifies the arithmetic algorithms to know that the numbers will always be in this form



2. Increases the accuracy of the numbers that can be stored in a word

e) explain the effects of using the proposed alternative representation instead of the eisting representation

the effects it can have is that you will the accuracy of the floating point will decrease if the mantissa has 1 less bit but the range will increase if the exponent increases by 1 bit.