Floating Point binary

Floating point binary have two parts, the mantissa and the exponent which are both written in 2s compliment.

Floating point is useful because we can get more accurate numbers.

Example

Mantissa   Exponent

1.000 1100 0100

As the exponent is 4 that means the decimal point moves four spaces to the right from its starting point which is always behind the MSB

10001.100= -16 + 1 + 1/2

= -14.5

 

 

To convert denary into floating point, you just do the same method backwards.

Example:

1.75=

-2  1  .  0.5  0.25

0  1  .  1     1

decimal point moves one to left so exponent = 1

Ans= 0111\0001