Question

Determine the 32-bit binary representation for floating point numbers in the form

± I.F x be

where I is the interger part,

F is the fraction,

b is the base, and

e is the exponent.

Using this format, represent the number 110011.0112 as a 32 bit floating point number.

Answer 1

Answer:Binary is a positional number system. It is also a base number system. For a refresher on this read our Introduction to number systems. As we move a position (or digit) to the left, the power we multiply the base (2 in binary) by increases by 1. As we move to the right we decrease by 1 (into negative numbers).

So in decimal the number 56.482 actually translates as:

5 * 101 50

6 * 100 6

4 * 10-1 4/10

8 * 10-2 8/100

2 * 10-3 2/1000

In binary it is the same process however we use powers of 2 instead.

So in binary the number 101.101 translates as:

1 * 22 4

0 * 21 0

1 * 20 1

1 * 2-1 1/2

0 * 2-2 0

1 * 2-3 1/8

Step-by-step explanation: