A signed number can be negative. Hardware has no minus sign, only bits, so a signed format is a rule saying which bit patterns stand for negative values.
The formats you'll meet:
- Two's complement: the MSB has weight −2ⁿ⁻¹. Used by essentially every modern processor.
- Sign-magnitude: the MSB is a sign flag and the other bits are the size. Easy to read, awkward for arithmetic.
- One's complement: negatives are bitwise inversions. Historical, with two zeros.
In all three, the MSB is the sign bit: 1 means negative.
"Signed" describes how you interpret bits, not the bits themselves. 11110000 is 240 as an unsigned number and −16 as a two's complement number. A program has to know which it means, which is why languages have separate signed and unsigned types and processors keep separate flags for each (see signed vs unsigned).
The price of signing: half the patterns go to negatives, so the largest positive value is roughly half of what the same bits reach unsigned.
1
−128
1
64
1
32
1
16
0
8
0
4
0
2
0
1