**Defined as :**

A binary number which is either positive or negative is known as *signed binary number.
*

Three representation schemes had been proposed for signed integers

* *

**Signed magnitude ****representation **

**
**Signed magnitude representation is the representation system for signed binary numbers in which the MSB represent the sign of number and the remaining bits represents the magnitude of the number.

**What is a sign bit ?
**The MSB of the signed binary number is called

*sign bit*.

If it is zero( 0 ) ,the number is positive.

when it is one ( 1 ), then the number is negative.

Now, In decimal number system plus sign is used to represent a positive number while negative sign shows a negative number.Since digital circuit can understand two numbers 0 and 1, So we must have the same symbols to indicate signed numbers.So

an additional bit is used to express sign of a number known as sign bit and it is placed as the most significant bit ,where 0 represent positive number and 1 represent a negative number.For example,

In an **4-bit signed number ****representation** , 0 1 1 1 represents a positive number and its magnitude is 7 . ( Left most bit MSB is 0 it represent that it is a positive number and the remaining bits 111 show its magnitude )

On the other hand, 1 1 1 1 represent a negative number and its magnitude is 7 .

( 1 in left most MSB indicates that the number is negative and the other remaining bits represent is value/magnitude )

This representation of numbers is known as* signed magnitude representation*.

**NOTE : while dealing with the binary numbers, we must take care to see the representation used in it.**

The **drawbacks** of sign-magnitude representation is :

Before we had a full range n-bit unsigned binary number,but now we have an n-1 bit signed binary number giving a reduced range of digits.

few examples shown below,

**Examples :
**Lets find out magnitude or decimal equivalent of the binary number assuming sign magnitude representation .

**Question :**

( 1 0 1 0 1 0 )_{2 }= ( ? )_{10 }

here ,6 bit signed binary number representation is used. So, left most bit ( MSB ) shows the sign bit (It is 1 ) and 1 means the number is negative. Now remaining five bits shows the magnitude of the number. So, decimal equivalent /magnitude of the binary number is 10.

**answer :**( 1 0 1 0 1 0 )

_{2 }= ( -1 0 )_{10 }

**Question :**

( 0 1 1 )_{2 }=( ? )_{10 }Here,3 bit signed binary number representation is used. So, left most bit ( MSB ) shows the sign bit (It is 0 ) and 0 means the number is positive. Now the remaining two bits shows the magnitude of the number. So, decimal equivalent /magnitude of the binary number is 3 .

**answer :**( 0 1 1 )

_{2 }= ( +3 )_{10 }= ( 3 )_{10}

**Question :**

( 0 1 1 1 1 )_{2 }=( ? )_{10
}Here,5 bit signed binary number representation is used. So, left most bit ( MSB ) shows the sign bit (It is 0 ) and 0 means the number is positive. Now the remaining four bits shows the magnitude of the number. So, decimal equivalent /magnitude of the binary number is 15 .

**answer :
**( 0 1 1 )

_{2 }= ( + 15 )

_{10 }= ( 15 )

_{10}

**Question :**

( 1 1 1 0 0 1 0 )_{2 }=( ? )_{10
}Here,7 bit signed binary number representation is used. So, left most bit ( MSB ) shows the sign bit (It is 1 ) and 1 means the number is negative. Now the remaining 6 bits shows the magnitude of the number. So, decimal equivalent /magnitude of the binary number is 50 .

**answer :
**( 1 1 1 0 0 1 0 )

_{2 }= ( – 50 )

_{10}

**Question :**

( 0 0 1 1 )_{2 }=( ? )_{10
}Here , 4 bit signed binary number representation is used. So, left most bit ( MSB ) shows the sign bit (It is 0 ) and 0 means the number is positive. Now the remaining three bits shows the magnitude of the number. So, decimal equivalent /magnitude of the binary number is 3 .

**answer :
**( 0 0 1 1 )

_{2 }= ( + 3 )

_{10}