A fixed number of bits can hold negative numbers too. The machine uses twos complement, where the top bit marks a negative value, so the same bits read as a negative number.
About 2 min of reading
Work with signed bits.
Print negative one in binary.
Before you run it, say out loud what it will print. Then open the answer.
Negate five by flipping and adding one.
Before you run it, say out loud what it will print. Then open the answer.
Read one byte signed and unsigned.
Before you run it, say out loud what it will print. Then open the answer.
Show the range of eight bits.
Before you run it, say out loud what it will print. Then open the answer.
Read the first example one line at a time. A line that prints shows what appears on screen; the rest set things up quietly.
Every modern machine stores signed integers this way. The rule is not a language detail, it is how hardware works.
The bytes are the same. Asking for a signed reading treats the top bit as a sign, and that choice changes the number.
print(-1)
print(bin(-1))Negative one is all ones. The top bit being 1 marks a negative value in twos complement.
print(~5 + 1)Flipping the bits of five and adding one gives its negative. That is the rule for negating a fixed row.
print(-3 + 3)A number plus its negative is zero with no special case. That is the reason twos complement was chosen.
print(-128, 127)Eight bits hold -128 to 127. There is one more negative than positive, because zero takes a slot.
print(int.from_bytes(b"\xff", "signed"))
print(int.from_bytes(b"\xff", "unsigned"))The same byte is -1 signed and 255 unsigned. The signed flag decides how the top bit is read.
print(0 == -0)There is one zero. A system with two zeros would waste a value, which is one reason this rule won.
print(7 + (-3))Subtracting is adding a negative. The machine only needs one adder, which is another gift of this rule.
print((-1).bit_length())The sign is not a separate flag, it is the top bit of the row. Reading it wrong turns a large positive into a negative.
Each one is defined here on this site. Open the entry for the full definition and the other words it points at.