Binary representation of signed integers

One simple idea is sign-magnitude representation.
- Given n bits, use the most significant (leftmost) bit for the sign("1" means negative), and the remaining n-1 bits to represent the magnitude.
- Examples (assuming 8 bits):
  33 is represented by 0010 0001
  -33 is represented by 1010 0001
- Remarks
  - with 16 bits, -33 is represented by
    1000 0000 0010 0001
  - Given n bits, there are
    2^n-1 - 1 possible positive number representations
    2^n-1 - 1 possible negative number representations
    and 2 zero representations (!)
```
1010 = -2
1001 = -1
1000 = -0
0000 = +0
0001 = +1
0010 = +2
```
ALTERNATIVELY a favored representation is 2's Complement representation that makes subtraction somewhat easier. We will look at this system later.