Digital Design_ Principles and Practices, Chegg Solution Manual_parte_026

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Step 1 of 2 2.021E In a radix r complement system, the complement of n-digit number D is obtained by subtracting it from as follows: According to context, in order to prove a 4n bit binary number B is represented by an n-digit hexadecimal number H and then the one's complement of B is represented by the 15's complement of H. It can be proved as shown below. Given that 4n bit binary number B is represented by an n-digit hexadecimal number H, which can be represented as follows. = The one's complement of B is represented by using equation (1) as follows: Step 2 of 2 Solve the above equation. Since The above equation also gives the value of 15's complement of H. Thus a 4n bit binary number B is represented by an n-digit hexadecimal number, then one's complement of B is represented by the 15's complement of H is proved. I's complement of complement of H