Digital Design_ Principles and Practices, Chegg Solution Manual_parte_030

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Step 1 of 4 2.025E In complement number representation Most Significant Bit (MSB) is sign bit. Hence the MSB represent the sign of the bit and its positional value is Consider an n-bit two's complement number X by standard formula, (1) Here, D is an n-bit integer in the form of Extend the n-bit representation to m-bit representation where m>n by appending m-n leftmost bits which are same as sign bits. (2) Step 2 of 4 Here, bits values are same. So, (3) Step 3 of 4 Step 1: Subtract the equation (2) from the equation (1). = Step 4 of 4 Continue simplifying the last expression in step1 using the relationship from equation (3), by adding right most two adjacent terms up to m-n terms to get the following expression: =0 Therefore, the two different representations of a number using m-bits and n-bits are equal where m > m bits are obtained by appending m-n sign bits at leftmost end.