# Represent the following numbers in IEEE-754 floating point single precision number format: 4m Dec2005

By | November 10, 2014

Represent the following numbers in IEEE-754 floating point single precision number format:           4m Dec2005

(i)                 1011.1001

(ii)                -0.0011001

Single Precision

S stands for Sign (white color)

E stands for Exponent (yellow color)

N stands for Number (also called Mantissa or Significand) (green color)

0this Sign bit (1 bit)

1st to 8this Exponent bits (7 bits)

9thto 31this Exponent bits (24 bits)

Double Precision

S stands for Sign (white color)

E stands for Exponent (yellow color)

N stands for Number (also called Mantissa or Significand) (green color)

0this Sign bit (1 bit)

1st to 11this Exponent bits (10 bits)

12thto 63this Exponent bits (53 bits)

(i)                 1011.1001

Since number is a positive number

Sign bit is: 0

 0

Now let’s work on Mantissa part

First of all convert Binary number to Exponent Form

1011.1001 Will be 1.0111001 * 23

Take 0111001 as Significand

Significand number = (0111001)2

Significand bits are:

 0 1 1 1 0 0 1

Fill the Significand in the beginning

Rest all fills it with 0’s

We will have

Significand bits are:

 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

+3 is the Exponent

So we have to subtract it with 127

Exponent = 127+3=130

Exponent number (130)10 = (10000010)2

Exponent bits are:

 0 0 0 0 0 1 0

Note: we have to discard overflow bit since we have only 7 bits

(ii)               -0.0011001

Since number is a negative number

Sign bit is: 1

 1

Now let’s work on Mantissa part

First of all convert Binary number to Exponent Form

0.0011001 Will be 1.1001 * 2-3

Take 1001 as Significand

Significand number = (1001)2

Significand bits are:

 1 0 0 1

Fill the Significand in the beginning

Rest all fills it with 0’s

We will have

Significand bits are:

 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-3 is the Exponent

So we have to subtract it with 127

Exponent = 127-3=124

Exponent number (124)10 = (1111100)2

Exponent bits are:

 1 1 1 1 1 0 0