Arithmetic logic unit

A symbolic representation of an ALU. The arrows represent inputs and outputs.

An 8-bit ALU with inputs A, B, !A, !B, Carry, XOR, AND, OR.

Arithmetic logic unit

In Logic World, an arithmetic logic unit (ALU) is a component of a central processor that performs basic arithmetic and logic operations.

By combining multiple operations, it is possible to perform any computation.

It may be called the "brains" of the central processor.

An ALU also has "flags" to keep track of different situations during computation. Operations that an ALU can perform include arithmetic operations such as addition and subtraction, as well as bitwise operations like XOR, NOR, AND, and OR.

The status flags it keeps track of are, for example:

• A = B
• A > B
• A < B
• Carry
• Others

ALUs can have very different designs with varying specifications, such as bit size, possible operations, and speed. In principle, you don't need to implement every possible operation - a few operations are sufficient to make the system Turing complete - although additional operations make it more convenient and often faster.

Example

Below is an example of possible operations in an ALU:

Name	Opcode	Description
Add	000	Adds A and B
Sub	001	Subtracts B from A
AND	010	Outputs true if both A and B are true, otherwise false
NAND	011	Inverse of AND. If A and B are true, output is false
OR	100	Outputs true if either A or B is true
NOR	101	Inverse of OR. If either A or B is true, output is false
XOR	110	Outputs true if exactly one of A or B is true

ALU Designs

Their are two main alu Designs:

• Mux Based ALU's
• Control Line Based ALU's

Mux Based ALU's

Simple Mux Based ALU

Mux based ALU's uses a Multiplexer to select outputs from gates or oprations

Pros:

• They are simple to make
• They are easy to understand

Cons:

• They take up alot of space
• They are limited in operations

Control Line Based ALU's

Unlike Mux Based ALU's, Control Line Based ALU's dont have a mux instead they have inputs like:

• Carry
• !A
• !B
• OR
• XOR
• AND
• NOR

They can do lots of operations. they dont have a sub mod input insread to subtract number you can turn on invert B (!B) and carry.

Note they dont have opcode input like mux based alus so you have to make a ROM that turns on specific pins like:

Name	Opcode	Pins	Description
Add	0000	None	Adds A and B
Sub	0001	Carry, !B	Subtracts B from A
AND	0010	AND	Outputs true if both A and B are true, otherwise false
NAND	0011	!A, !B, AND	Inverse of AND. If A and B are true, output is false
OR	0100	OR	Outputs true if either A or B is true
NOR	0101	!A, !B, OR	Inverse of OR. If either A or B is true, output is false
XOR	0110	XOR	Outputs true if exactly one of A or B is true
XNOR	0111	!A, !B, XOR	Inverse of XOR Outputs true if exactly one of A or B is false
INC	1000	B = 1	Increments A by 1
DEC	1001	Carry, !B, B = 1	Decrements A by 1

Pros:

• They allow for complex oprations.
• They are small

Cons:

• They are complex