**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

**or**

*Mantissa***(green color)**

*Significand)*

** 0^{th}**is Sign bit (1 bit)

** 1^{st }to 8^{th}**is Exponent bits (7 bits)

** 9^{th}to 31^{th}**is Exponent bits (24 bits)

**Double Precision**

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

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

N stands for ** Number (**also called

**or**

*Mantissa***(green color)**

*Significand)*

** 0^{th}**is Sign bit (1 bit)

** 1^{st }to 11^{th}**is Exponent bits (10 bits)

** 12^{th}to 63^{th}**is 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 * 2 ^{3}*

Discard 1.

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}

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** *

(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}*

Discard 1.

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 |