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Lesson 11:Design of ALU

Chapter 03: Computer Arithmetic

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Objective

Understand the units in ALU

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ALUs

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ALU

Each processor has an ALU

At ALU the arithmetic and logic operationsperformed.

ALU performs two types of operations.

1. Fixed point operations 2. Floating point operations

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ALU Design

Combinational Logic

Circuits-based ALUs

Sequential Logic Circuits

Based ALUs

Bit SliceProcessors

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ALUs

Fixed Point ALUs

Floating Point Point

ALUs

Bit Slice Processors Based

ALUs

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ALU Operations

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ALU two types of operations

1. Fixed point operations

2. Floating point operations

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Fixed Point (Integer) ALU Operations

Add

Unsigned Multiply

ANDAdd with carry

Subtract

Multiply

Subtract with

Borrow

Divide Unsigned Divide

OR

XOR

NOT

L-Shift

R-Shift

Arth R-Shift

TEST

CMP

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Floating Point ALU Operations

FAdd FSub FMul FDiv

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Complex ALU Operations

MAC VLIW operations

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Common arithmetic operations

1. Addition, subtraction

2. Addition-with-carry (from a previousoperation)

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Common arithmetic operations

3. Subtraction with borrow from a previousoperation. Common circuit for addition and

subtraction.

ALU common flag for carry and borrow(many processors) or common flag for carryand not-borrow (8096)

Carry flag an output carry from a chain of bit-adders

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Common arithmetic operations

4. Division

5. Increment and decrement6. Logical shift left and logical shift right

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Logical Shift

0b00100111 after logical left shift

= 0b01001110 0b00100111 after logical right shift

= 0b00010011

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Common arithmetic operations

Arithmetic shift left and logical shift right

Arithmetic shift left and logical shift left same. Arithmetic shift right and logical shift right are

different.

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Arithmetic Shift

0b00100111 after arth. left shift

= 0b01001110 0b00100111 after arth. right shift

= 0b00010011

0b10100111 after arth. right shift

= 0b11010011

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Common logic operations

NOT

AND, OR, XOR COMPARE

TEST

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Logic Operations 0b00100111 after NOT

= 0b11011000

0b00100111 and 0b11011001 after AND =

0b00000001

0b00100111 and 0b11011001 after OR =0b11111111

0b00100111 and 0b11011001 after XOR =

0b11111110

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Compare Operations

0b00100111 and 0b11011001 after operation

Sign Flag = 1, Zero Flag = 0

0b11011001 and 0b 00100111 after operation

Sign Flag = 0, Zero Flag = 0

0b 00100111 and 0b 00100111 after operationSign Flag = 0, Zero Flag = 1

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TEST Operations

0b00100111 and 0b11011000 after operation

Test Flag = 0, Zero Flag = 1

0b11011001 and 0b 11011001 after operation

Test Flag = 1, Zero Flag = 0

0b 00100111 and 0b 00000111 after operationTest Flag = 0, Zero Flag = 0

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Combinational Logic Circuits-based ALUs

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An ALU using combinational circuits

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Combinational Circuits Based ALU

k-Input X Select Circuitk-Input Y

XOR OR ADD

ResultFlags

Bus

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Sequentias Circuits-based ALUs

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An ALU using sequential circuit

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Sequential LogicCircuits Based ALU

k-Input X Select/Controlk-Input Y

AND OR ADD

ResultFlags

Bus

Control Unit Registers

For

intermediateresults

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Bit Slice Circuits-based ALUs

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Bit Slice Processors Circuit Based ALU

k-Input X Select/Controlk-Input Y

P2

P3 P5

ResultFlags

Bus

P1

P4

For

intermediateresults

Bit Slice ALUs

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Bit Slice

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Summary

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ALUs

Fixed Point ALUs

Floating Point Point

ALUs

Bit Slice Processors Based

ALUs

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ALU Operations

Add

Unsigned Multiply

ANDAdd with carry

Subtract

Multiply

Subtract with

Borrow

Divide Unsigned Divide

OR

XOR

NOT

L-Shift

R-Shift

Arth R-Shift

TEST

CMP

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ALU Design

Combinational Logic

Circuits-based ALUs

Sequential Logic Circuits

Based ALUs

Bit Slice

Processors

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End of Lesson 11 on

Design of ALU