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.

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 * 10150

6 * 1006

4 * 10-14/10

8 * 10-28/100

2 * 10-32/1000

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

So in binary the number 101.101 translates as:

1 * 224

0 * 210

1 * 201

1 * 2-11/2

0 * 2-20

1 * 2-31/8

Explanation:

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