Numbers Outside of Address Range (Sign-Magnitude Rep.)

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SUMMARY

The discussion centers on the use of sign-magnitude representation for 8-bit numbers, specifically addressing the range of values that can be represented. The maximum range for an 8-bit sign-magnitude representation is confirmed to be -128 to 127, with the left-most bit serving as the sign bit. A participant clarifies that 80 can indeed be represented using 7 bits, allowing for the correct interpretation of the range. This understanding resolves initial confusion regarding the dual role of the left-most bit.

PREREQUISITES
  • Understanding of binary number systems
  • Familiarity with sign-magnitude representation
  • Knowledge of bit manipulation and representation
  • Basic concepts of number ranges in computing
NEXT STEPS
  • Research the implications of sign-magnitude representation in computer architecture
  • Learn about two's complement representation and its advantages
  • Explore the effects of bit length on number representation
  • Study how different number systems handle overflow and underflow
USEFUL FOR

Computer science students, software engineers, and anyone interested in understanding binary representations and their applications in computing.

KongMD
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Homework Statement



+35 + -80 with only 8-bits using sign-magnitude representation

Homework Equations


The Attempt at a Solution



Why is this possible? Allowing for one sign bit, the maximum range (in my mind) should be -63 < N < 63. I can see from my notes, however, that the limits of an 8-bit addressing scheme for sign-magnitude representation is -127 < N < 127. How can the left-most bit be both the sign and part of the number?! I'm not asking for anyone to do the problem for me, but I just want to understand why the left-most bit can perform both functions.

EDIT: I think I figured it out. 80 can be represented in 7-bits - I must've had my counting off somewhere. Sorry!
 
Last edited:
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Yes, your counting was off. With 7 bits you can represent 0 through 127. With the eighth bit for the sign, you can represent the numbers -128 through 127.
 

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