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Step of 5 2.030E In a n-bit two's complement representation, the range of integer values is, Two's complement representation of integer X, (1) Two's complement representation of integer Y, (2) Step 2 of 5 Multiply two's complement number X with Y. (3) Substitute for X. = Simplify the equation further. Step of 5 Case Consider both X and Y are positive and their maximum values are (4) From equation (4), it is evident that product can be represented with less than 2n number of bits. Since the positive result is less than Step of 5 Case II: Consider X as positive integer with maximum value and Y as negative integer with the maximum value (5) Case III: Consider X as negative integer with maximum value and Yas positive integer with the maximum value (6) From equation (5) and (6), the product can be represented with less than 2n number of bits. Since the negative value is less than Step of 5 Case IV: Consider both X and Y are negative integers and their maximum values are The product X-Y cannot be represented with less than 2n number of bits. Since the value is greater than But it can be represented with 2n number of bits in two's complement representation. Hence, in case IV that is both X and Y are negative integers and their maximum value is equal to needs 2n bits for its representation.