How does the number of bits affect the biggest possible number you can hold?

[If you have 8 bits you can hold: (1+2+4+8+16+32+64+128) as your biggest value and 0 as your smallest. This gives a range of 0-255, or 256 different possible values. Each time you add another bit you double the range of values available, i.e. moving to 9 bits would give us a range of 512]