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

[KongMD]

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!

 

[Mark44]

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.