Signed Numbers Representation

 Signed Numbers Representation

                In general, we represent the positive numbers without any sign indication and negative numbers with ‘minus’(negative) sign before them. But these are not applicable for computing in the digital systems like, computers, as the data is represented in binary number system. So to represent the sign a special notation is required.

    Positive signed binary numbers

                The binary numbers having their MSB (Most Significant Bit) 0 are called “Positive signed binary numbers”.

     Negative signed binary numbers

                The binary numbers having their MSB (Most Significant Bit) 1 are called “Negative signed binary numbers”.

We can represent their range only from – (2^(n-1) - 1) to +(2^(n-1) – 1)

     Signed & Magnitude Representation

                The binary numbers which can be identified by their MSB whether they are positive or negative are called “Signed binary numbers”.

                Eg           1001               +9 (positive) 

                                 1001               -1 (negative)

·         Positive number is represented with “0” at its MSB.

·         Negative number is represented with “1” at its MSB.

          One’s complement representation

                            One’s complement is another way to feeding the negative binary number to the computer. In one’s complement method, the positive binary numbers are unchanged. But the negative numbers are represented by talking one’s complement of unsinged positive numbers.

                            A positive number always starts with 0, at its MSB while a negative number always starts with 1, at its MSB.

                Eg           35 is represented as 100011₂

                                In 8-bit notation, it is represented 0010 0011₂

                                Now 35 is represented in one’s compliment as 1101 1100₂

                Eg           10 is represented as 1010₂

                                In 8-bit notation, it is represented 0000 1010₂

                                Now 10 is represented in one’s compliment as 1111 0101₂

    Two’scomplement representation

                The process of finding is similar to the process of calculating 10’s complement of decimal numbers. To find the two’s compliment of a binary number, first we should find the one’s compliment of that number and later “1” is added to the one’s compliment. Two’s compliment representation of positive numbers is same is same as the representation of one’s compliment and singed magnitude representation.

                Eg           42 is represented as 101010₂

                                In 8-bit notation, it is represented as 0010 1010₂

                                Now 42 is represented in one’s compliment as 1101 0101₂

                                Adding 1 to it

                                The result is 1101 0110₂

                Eg           99 is represented as 1100011₂

                                In 8-bit notation, it is represented as 0110 0011₂

                                Now 99 is represented in one’s compliment as 1001 1100₂

                                Adding 1 to it

                                The result is 1001 1101