Unsigned
Description: Cannot represent number with negative sign, cannot handle calculation with negative sign
Range: $0, 2^n-1$
To dec: $bit * 2^n + ....$
To hex: devide by 4 items per group, then, transfer each group's bit to hex
Dec to: keep dividing by 2, result will be remainder in reversed order
Hex to: transfer each hex number into 4-bit binary, splicing them then
Overflow: result will be $(NUMBER) mod 2^n$, where as $n$ means the n-bit.
Complement: add 0 till reach limit
Signed/2's Complement
Description: can represent sign, can do calculation with different sign directly
Range: $-2^{n-1}, 2^{n-1}-1$
To dec:
- if positive, do tranfering like unsigned
- if negative, do transfering like unsigned but treat the first bit as $-2^n * bit$ instead of $2^n * bit$. The second way is to remove first bit, flip all bits, add one, then do like unsigned. remember to add the negative sign to the final result
Dec to:
- if positive, do tranfering like unsigned, then add 0 to front
- if negative, remove first bit, flip all bits, add one, then do like unsigned. remember to add the negative sign to the final result
Overflow: determine by checking if the sign make sense, see if it seat in the range, if so, no overflow.
the overflow result determined by the sign:
- if positive, the result will be $NUMBER - 2^n$
- if negative, the result will be $NUMBER + 2^n$
To check if overflow happens in calculation, refer to the image below:
remember to pay attention to the direction.
