Here's an example, which assumes (since it's always true for Mac programming) that we're using the two's complement method for storing signed numbers. We're pretend we have only 4 bits in our integers:

How the 16 possible unsigned bit patterns are interpreted:

0000 means 0

0001 means 1 (which is the same as +1)

0010 means 2 (which is the same as +2)

0011 means 3 (which is the same as +3)

0100 means 4 (which is the same as +4)

0101 means 5 (which is the same as +5)

0110 means 6 (which is the same as +6)

0111 means 7 (which is the same as +7)

1000 means 8 (which is the same as +8)

1001 means 9 (which is the same as +9)

1010 means 10 (which is the same as +10)

1011 means 11 (which is the same as +11)

1100 means 12 (which is the same as +12)

1101 means 13 (which is the same as +13)

1110 means 14 (which is the same as +14)

1111 means 15 (which is the same as +15)

Conclusion: We can represent 16 different integers but all of them are positive.

How the 16 possible signed bit patterns are interpreted:

0000 means 0

0001 means 1 (which is the same as +1)

0010 means 2 (which is the same as +2)

0011 means 3 (which is the same as +3)

0100 means 4 (which is the same as +4)

0101 means 5 (which is the same as +5)

0110 means 6 (which is the same as +6)

0111 means 7 (which is the same as +7)

1000 means -8

1001 means -7

1010 means -6

1011 means -5

1100 means -4

1101 means -3

1110 means -2

1111 means -1

Conclusion: We can represent 8 different non-negative integers and 8 different negative integers.

Notice that the **unsigned bit patterns** don't really represent **unsigned numbers**. Each bit pattern in both sets *represents* an integer, and integers by nature always have a sign. People tend to gloss over the distinction.