# FLOATING POINT AND SIGNED NUMBERS (DIGITAL ELECTRONICS)

**FLOATING POINT AND SIGNED NUMBERS (DIGITAL ELECTRONICS)**

Floating piont and signed numbers are very impotant topics of digital electronics.so first of all we have to know about defination of floatinf point ans signed numbers.

**FLOATING POINT:**

The number which has both an integer and a fractional part is called as floating point number.The floating point number can be used to represent large as well as small fraction or mixed number.Genrally floating point represents an method of approximation to real number in such a way that they can support a wide range of values. Genral form of a number can be represented as

N=±m×b^{±}^{e}

M=mantissa

B=base of number

E=exponent

In the whole expression the first number part is called as mantissa which is signed fixed point number and the second part is called as exponent that is either decimal or binary species position.

**DISADVANTAGES:**

- Floating point nuber suffers from the loss of precession when it is represented with a fixed number of bit.Ex 34 or 64 bit.
- Integer arithmatic is very much efficient than floating nuber arithmatic.

**SIGNED NUMBERS:**

Signed numbers or signed integer are the numbers which represents zero,positive and negative integers.There are three representation available for signed integers :

- Sign magnitude representation.
- 1’s comlement representation.
- 2’s complement representation

**SIGN MAGNITUDE REPRESENTATION:**

The most significant in sign magnitude representation is the sign bit,having value 0 representing positive integer and 1 for negative integer.And the remaining n-1 bits represents the absolut or magnitude of the integers

EXAMPLE:Let n=8,and its binary binary representation is 0 100 0001B Sign bit=0àpositive

Abolute value=100 0001B=65D

So the integer is +65D

**1’s complement representation:**

Here also sign bit is significant where 0 represents positive integer and 1 for negative integer.And the remaining n-1 bit represents the absolute value or magnitude of the integer

- For negative integer the absolute value is=magnitude of the inverse of n-1 bit binary pattern
- And for positive integer the absolute value is=magnitude of n-1 bit binary pattern

EXAMPLE:Let n=8 and binary representation is 1 000 0001B

Sign bit=1ànegative

Absolute value is complement of 000 0001B=111 1110B=126D

So the integer is -126D

**2’s complement representation:**

As above mentioned here also sign bit is important where0àpositive integer and 1ànegative integer .And the remaining n-1 bit represents the absolute value or magnitude of the integer.

- For negative integer the absolute value is=magnitude of the inverse of n-1 bit plus one binary pattern
- And for positive integer the absolute value is=magnitude of n-1 bit binary pattern

IMPORTANT QUESTIONS:

1-Describe floating point?

Ans-The number which has both an integer and a fractional part is called as floating point number.The floating point number can be used to represent large as well as small fraction or mixed number.Genrally floating point represents an method of approximation to real number in such a way that they can support a wide range of values. Genral form of a number can be represented as

N=±m×b^{±}^{e}

M=mantissa

B=base of number

E=exponent

2-What are the disadvantages of floating point?

Ans- The disadvantages of floating point are as follow

- Floating point nuber suffers from the loss of precession when it is represented with a fixed number of bit.Ex 34 or 64 bit.
- Integer arithmatic is very much efficient than floating nuber arithmatic.

3-How many representation are available for signed numbers?

Ans-There are three representation available for signed integers :

- Sign magnitude representation.
- 1’s comlement representation.
- 2’s complement representation

4-Describe 1’s complement representation with an example.

Ans-

Here sign bit is significant where 0 represents positive integer and 1 for negative integer.And the remaining n-1 bit represents the absolute value or magnitude of the integer

- For negative integer the absolute value is=magnitude of the inverse of n-1 bit binary pattern
- And for positive integer the absolute value is=magnitude of n-1 bit binary pattern

EXAMPLE:Let n=8 and binary representation is 1 000 0001B

Sign bit=1ànegative

Absolute value is complement of 000 0001B=111 1110B=126D

So the integer is -126D

5-If n=8 and binary representation is 1 111 1111B find out the integer for 2’s complement representation?

Ans-Sign bit is 1–>negative

Absolute value is the complement of 111 1111B plus one=000 0000B+1B=1D

So the integer is -1D

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This article comprises of about the topics covered in floating point and signed numbers. These are very important topics of digital electronics.

In computing, floating point describes a method of representing an approximation to real numbers in a way that can support a wide range of values. The numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The detail about this convertion is given in this article.