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======Signed vs. Unsigned Values======

^  Binary (Base 2)  ^  Signed Decimal (Base 10)  ^  Unsigned Decimal (Base 10)  ^  Hexadecimal (Base 16)  |
|  0 0 0 0  |  0  |  0  |  0x0  |
|  0 0 0 1  |  1  |  1  |  0x1  |
|  0 0 1 0  |  2  |  2  |  0x2  |
|  0 0 1 1  |  3  |  3  |  0x3  |
|  0 1 0 0  |  4  |  4  |  0x4  |
|  0 1 0 1  |  5  |  5  |  0x5  |
|  0 1 1 0  |  6  |  6  |  0x6  |
|  0 1 1 1  |  7  |  7  |  0x7  |
|  1 0 0 0  |  -8  |  8  |  0x8  |
|  1 0 0 1  |  -7  |  9  |  0x9  |
|  1 0 1 0  |  -6  |  10  |  0xA  |
|  1 0 1 1  |  -5  |  11  |  0xB  |
|  1 1 0 0  |  -4  |  12  |  0xC  |
|  1 1 0 1  |  -3  |  13  |  0xD  |
|  1 1 1 0  |  -2  |  14  |  0xE  |
|  1 1 1 1  |  -1  |  15  |  0xF  |

A signed value is when we take a bit (usually the //most significant bit//) and reserve it for the sign. This **shifts** the representable range of values, straddling 0. We still have the **same** quantity of values as in the unsigned range, we just represent them differently.

We use a technique called **two's complement** to represent signed values (the negative values, specifically).

In this case, a leading 0 indicates a positive value, and a leading 1 indicates a negative value.

For example- 1000, leading one, so negative. Negative what?

Step one- invert: 1000 becomes 0111.

Step two- add one: 0111+1 = 1000. This is a **-8**.

Another example: 1101.

Invert: 0010

Add one: 0010+1 = 0011 (this is a 3, and we know we started with a leading 1, so 1101 is **-3**).