Category: Most Negative 7-bit

What is the decimal value of the most negative number that can be represented by a 7-bit two's complement binary number? Your answer must start with a - sign. The rest of your answer must only contain decimal digits.

Question

Category: Most Negative 7-bit

What is the decimal value of the most negative number that can be represented by a 7-bit two's complement binary number? Your answer must start with a - sign. The rest of your answer must only contain decimal digits.

BlackTom AI · Accepted Answer

Restating the task: determine the decimal value of the most negative number in a 7-bit two's complement representation, with the answer starting with a minus sign.

First, recall how two's complement ranges work for n bits. In two's complement, the range is from -2^(n-1) to +2^(n-1) - 1. This arises because the most significant bit serves as the sign bit, and the negative range goes down to -2^(n-1).

For n = 7, compute the extreme values: -2^(7-1) = -2^6 = -64 is the most negative value, and the largest positive value is 2^6 - 1 = 63.

Therefore, the most negative number representable with 7 bits is -64. In binary, that value is represented as 1000000, where the leading 1 indicates the negative sign in two's complement and the remaining zeros complete the magnitude.

Why not -65 or some other value? Because -65 is outside the representable range for 7-bit two's complement; the system only supports down to -64. Similarly, 64 cannot be represented as a positive value because the maximum positive is 63.

Since the question requires the answer to start with a minus sign and to be shown in decimal digits, the correct decimal representation is -64.

4520_COMP_SCI_X_0005 Practice Exam

Category: Most Negative 7-bit What is the decimal value of the most negative number that can be represented by a 7-bit two's complement binary number? Your answer must start with a - sign. The rest of your answer must only contain decimal digits.

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