Question at position 8 What is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. AnswerWhat is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. [input]

Question

Question at position 8 What is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. AnswerWhat is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. [input]

BlackTom AI · Accepted Answer

To determine the largest positive number representable in 10-bit 2's complement, we first recall the general range for n-bit 2's complement numbers: from -2^(n-1) to 2^(n-1) - 1. Here, n = 10, so the range is -2^9 to 2^9 - 1, which equals -512 to 511. This means the maximum positive value cannot exceed 2^9 - 1.

Next, compute 2^9 - 1: 2^9 is 512, so 2^9 - 1 equals 511. Therefore, the largest positive number that can be represented in 10-bit 2's complement is 511.

A quick check helps ensure there isn't any larger positive value: attempting to represent 512 would require a bit pattern that exceeds the maximum positive value for 10-bit 2's complement, and such a pattern would correspond to a negative number (-512) due to how the sign bit and two's complement encoding work.

In summary, the maximum positive value is 511, consistent with the established range for 10-bit 2's complement numbers.

Question at position 8 What is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. AnswerWhat is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. [input]

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