# finding smallest and largest number given n binary bits

• Dec 10th 2011, 08:25 PM
Jskid
finding smallest and largest number given n binary bits
Given n bits that can hold 0s or 1s what is the largest and smallest integer they can hold? I know the formula $min=-2^{n-1}, max=2^{n-1}-1$ but is that only for numbers stored using two's compliment? Is there a formula for one's compliment and signed magnitude? If a number is unsigned then it would be 2^n right?
• Dec 11th 2011, 08:49 AM
emakarov
Re: finding smallest and largest number given n binary bits
Quote:

Originally Posted by Jskid
Given n bits that can hold 0s or 1s what is the largest and smallest integer they can hold? I know the formula $min=-2^{n-1}, max=2^{n-1}-1$ but is that only for numbers stored using two's compliment?

Yes.

Quote:

Originally Posted by Jskid
Is there a formula for one's compliment and signed magnitude?

"An n-bit ones' complement numeral system can represent integers in the range $-(2^{n-1}-1)$ to $2^{n-1}-1$" (Wikipedia). For the sign-and-magnitude method, the interval is the same because n - 1 bits represent the absolute value.

Quote:

Originally Posted by Jskid
If a number is unsigned then it would be 2^n right?

The largest representable integer is not $2^n$. Consider the example when n = 3 and the largest integer is $111_2$.