# The range of numbers of an n-bit cell in general?

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• February 2nd 2014, 11:39 AM
lamentofking
The range of numbers of an n-bit cell in general?
With unsigned binary representation, what is the range of numbers as written in binary
and in decimal for the following cells?

(e)an n-bit cell in general

This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
in binary 000-111 and decimal 0 to 7.
• February 2nd 2014, 12:09 PM
romsek
Re: The range of numbers of an n-bit cell in general?
Quote:

Originally Posted by lamentofking
With unsigned binary representation, what is the range of numbers as written in binary
and in decimal for the following cells?

(e)an n-bit cell in general

This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
in binary 000-111 and decimal 0 to 7.

in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

for binary k=2
for decimal k=10
• February 5th 2014, 09:39 AM
lamentofking
Re: The range of numbers of an n-bit cell in general?
Quote:

Originally Posted by romsek
in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

for binary k=2
for decimal k=10

And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.
• February 5th 2014, 10:41 AM
romsek
Re: The range of numbers of an n-bit cell in general?
Quote:

Originally Posted by lamentofking
And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.

$[-2^{n-1}, 2^{n-1}-1]$ for an n bit, binary string, so for n=7 the range is $[-2^6,2^6-1]=[-64,63]$