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.

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 k^{n} numbers so if 0 is to be your first number you have the range of [0,k^{n}-1].

for binary k=2

for decimal k=10

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 k^{n} numbers so if 0 is to be your first number you have the range of [0,k^{n}-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.

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.

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