256

256

Every pattern of the 256 patterns has been assigned an integer to represent.

The
algorithm that creates the representation of the negative of an integer
works with both positive and negative integers.
Start with `N`

and form its two's complement:
you get `-N`

.
Now complement `-N`

and you get the original `N`

.

0110 1101 reflect → 1001 0010 add one → 1001 0011 1001 0011 reflect → 0110 1100 add one → 0110 1101

With N-bit two's comp representation,
the high order bit is "0" for positive
integers and "1" for negative integers.
This is a fortunate result.
The high order bit is sometimes called the **sign bit**.
But it is not really a sign
(it does not play a separate role from the other bits).
It takes part in the "binary addition algorithm" just as any
bit.

Does the following **four-bit** two's complement represent
a negative or a positive integer?

1001