Arithmetic Logic Units: Understanding ALUs and Their Role in Computer Systems, Study notes of Engineering

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ENGIN 112

Intro to Electrical and Computer Engineering

Lecture 33

Arithmetic Logic Unit (ALU)

Overview

°Main computation unit in most computer systems

°ALUs perform a vaiety of different functions

• Add, subtract, OR, AND…

°Example: ALU chip (74LS382)

• Has data and control inputs

°Individual chips can be chained together to make larger

ALUs

°ALUs are important parts of datapaths

• ROMs often are usd in the control path

°Build a data and control path

Arithmetic Logic Unit

°Arithmetic logic unit

functions

• Two multi-bit data inputs
• Function indicates action (e.g. add, subtract, OR… )

°DataOut is same bit

width as multi-bit inputs

(DataA and DataB)

°ALU is combinational

°Conditions indicate

special conditions of

arithmetic activity (e.g.

overflow).

ALU

Function Conditions

DataA DataB

DataOut

Think of ALU as a number of other arithmetic and logic blocks in a single box! Function selects the block

Adder Subtract

… AND

ALU Integrated Circuit

°Integrated circuit –off-the-shelf components

°Examine the functionality of this ALU chip

Performs 8 functions

Expanding the ALU

°Multi-bit ALU created by connecting carry output of

low-order chip to carry in of high order

Eight-bit ALU formed from 2 four-bit ALUs

Datapath components

°Tri-state buffer

°Loadable register

In Out

Enable

If Enable asserted, Out = In Otherwise Out open-circuit

Clk Load

Data stored on rising edge if Load is asserted (e.g. Load = 1)

Using a Datapath

° Consider the following computation steps

1. ADD A, B and put result in A
2. Subtract A, B and put result in B
3. OR A, B put result in A

• Repeat starting from step 1

Determine values for Function, LoadA, LoadB

Function

LoadA A B LoadB

ALU

Modeling Control as a State Machine

° Consider the following computation steps

1. ADD A, B and put result in A
2. Subtract A, B and put result in B
3. OR A, B put result in A

• Repeat starting from step 1

Determine values for Function, LoadA, LoadB

S0 S1 S

Model control as a state machine. Determine control outputs for each state

ROM Implementation of State Machine

States S0 = 00 S1 = 01 S2 = 10

Present State Next State Function LoadA LoadB

PS

NS

0101110 1001001 0010110

ROM

Function, LoadA, LoadB

Note: No minimization! One line in ROM for each state

Putting the Control and Datapath Together

PS

NS

0101110 1001001 0010110

ROM

Function

LoadA A B LoadB

ALU

Summary

°ALU circuit can perform many functions

• Combinational circuit

°ALU chips can be combined together to form larger

ALU chips

• Remember to connect carry out to carry in

°ALUs form the basis of datapaths

°ROMs can form the basis of control paths

°Combine the two together to build a computing circuit

°Next time: more data and control paths