# 2.3 Multi-level signalling (M-ary signalling)

## The relationship between bits and symbols #### It is now very uncommon to design modems that use only binary (two symbol) signalling, with users demanding ever higher data rates in the same channel bandwidth. It has already been mentioned that some modern dial-up modems use over 1024 signalling states. |

#### The number of symbol states needed to uniquely represent any pattern of n bits is given by the simple expression: #### M = 2n symbol states

#### For example, a group of three bits can be represented by one of: #### M = 23 = 8 symbol states 4 bits by M = 24 = 16 symbol states 5 bits by M = 25 = 32 symbol states #### and so on.