Signed binary numbers

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

  1. Sign magnitude representation
  2. 1’s Complement representation
  3. 2’s Complement representation

 

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 ) =  (  -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 ) =  ( +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 ) =  ( + 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 ) =  ( – 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 ) =  ( + 3 )10

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