185 stored as a signed 8-bit number?

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Discussion Overview

The discussion revolves around the representation of signed 8-bit integers, specifically focusing on the values 185, 122, 151, and 214 in different formats (sign-magnitude and two's complement). Participants express confusion regarding the maximum representable value in signed 8-bit format and the implications for overflow and underflow in related exercises.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the maximum number representable in signed 8-bit format is 127, calculated as 2^7−1.
  • Others express confusion about the exercises that include numbers (185, 122, 151, 214) that exceed this maximum, questioning the validity of the assumptions in the textbook.
  • One participant highlights that three of the numbers listed are too large to fit in 8 bits, given the constraints of signed representation.
  • Another participant points out that the exercises ask about overflow or underflow, raising concerns about how to address these questions with the provided numbers.
  • A request is made for a sample exercise and the textbook's answer to clarify the situation further.

Areas of Agreement / Disagreement

Participants generally agree that the maximum representable value for signed 8-bit integers is 127, but there is disagreement regarding the validity of the textbook exercises and how to approach the questions of overflow and underflow with the given numbers.

Contextual Notes

The discussion highlights limitations in the assumptions made by the textbook, particularly regarding the representation of numbers that exceed the maximum for signed 8-bit integers. There is also an unresolved aspect concerning how to handle overflow and underflow in the context of the exercises.

joel amos
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Several exercises in my textbook start with assumptions that confuse me. For example:

  • Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format.
  • Assume 151 and 214 are signed 8-bit decimal integers stored in two's complement format.
I am then to go on to find the sum or difference (varies by exercise) of the numbers and state if there is overflow, underflow, or neither.

But...isn't the maximum number that can be represented here 2^7−1=127?
 
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joel amos said:
Several exercises in my textbook start with assumptions that confuse me. For example:

  • Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format.
  • Assume 151 and 214 are signed 8-bit decimal integers stored in two's complement format.
I am then to go on to find the sum or difference (varies by exercise) of the numbers and state if there is overflow, underflow, or neither.

But...isn't the maximum number that can be represented here 2^7−1=127?
These questions don't make sense to me, either. 127 is the largest number that can be stored as a signed 8-bit integer. So three of the numbers listed above are already too large to fit in 8 bits (with one bit for the sign).
 
joel amos said:
But...isn't the maximum number that can be represented here 2^7−1=127

And doesn't the question ask you if there are overflows or underflows?
 
joel amos said:
Several exercises in my textbook start with assumptions that confuse me. For example:

  • Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format.
  • Assume 151 and 214 are signed 8-bit decimal integers stored in two's complement format.
I am then to go on to find the sum or difference (varies by exercise) of the numbers and state if there is overflow, underflow, or neither.

But...isn't the maximum number that can be represented here 2^7−1=127?
Can you provide a sample: one exercise, together with the textbook's answer?
 

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