Arithmetic logic unit
An arithmetic logic unit (usually referred to as an ALU) is the part of a CPU in which calculations (both numerical and logical, hence the name) are carried out.
Typical operations performed by an ALU are addition, logical AND, etc. In early machines, the ALUs could not perform a full range of mathematical operations; multiplication (and division), for example, was often not provided - or performed in another, often-optional, unit. Floating point was also typically supported by a separate unit.
A relatively early 74 series MSI TTL chip, the 74181, provided a 4-bit ALU, with a full complement of 16 different arithmetical and logical operations on the two operands. Although popular once it was introduced, earlier low-end machines (e.g. the PDP-11/20) often had less capable ALUs, in order to keep the chip count, and thus the cost, down.