The largest positive number that can be represented in 13 bits for the two cases are
A) Unsigned number
The largest unsigned no can be represented with 13bits as
[tex](2)^n - 1 = (2)^{13} - 1 = 8191[/tex]
In Binary - [tex](1111111111111)_2[/tex]
In decimal - [tex](8191)_{10}[/tex]
In hexadecimal - [tex](1FFF)_{16[/tex]
B) Signed number
The largest signed no can be represented with 13bit as
[tex]2^n = 2^{13} = 8192[/tex]
The range is from [tex](2^n-1)[/tex]
therefore, the maximum value is [tex](4096)_{10}[/tex]
In binary - [tex](1000000000000)_2[/tex]
In hexadecimal - [tex](1000)_{16}[/tex]
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