**Represent the number (-26.5) _{10} as a floating point binary number with 24 bits. The normalized fraction mantissa has 16 bits and the exponent has 8 bits. Make and state suitable assumptions, if any 5m Dec2005**

First of all draw the **24 bits ****precision representations**

S stands for ** Sign **(white color)

E stands for ** Exponent **(yellow color)

N stands for ** Number (**also called

**or**

*Mantissa***(green color)**

*Significand)*Then to represent we have (-26.5)_{10} using **24 bits ****precision representations**

Since number is a ** negative** number

Sign bit is: 1

1 |

Now let’s work on Mantissa part

Convert 26 into binary form *i.e* 11010

Remaining is fraction part 0.5

Now we multiply fraction value with 2 till we get whole number 1 at the end.

We reach 1 so we stop

Write number from top to bottom

We get 0.5 = 1

Number (-26.5)_{10 }= (11010.1)_{2}

Convert Binary number to Exponent Form

**11010.1 **Will be *1.10101 * 2 ^{4}*

Discard 1.

Take ** 11010** as Significand

Significand number _{=} (11010)_{2}

Significand bits are:

1 | 1 | 0 | 1 | 0 |

Fill the Significand in the beginning

Rest all fills it with 0’s

We will have

Significand bits are:

1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

+4 is the Exponent

So we have to subtract it with 127

Exponent = 127+4=130

Exponent number (130)_{10 }= (10000010)_{2}

Discard overflow bit

Exponent bits are:

0 | 0 | 0 | 0 | 0 | 1 | 0 |

* *

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