HCL and ALU

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Overview of Logic Design Fundamental Hardware Requirements

– Communication: How to get values from one place to another– Computation– Storage

Bits are Our Friends– Everything expressed in terms of values 0 and 1– Communication

• Low or high voltage on wire

– Computation• Compute Boolean functions

– Storage• Store bits of information

Digital Signals

– Use voltage thresholds to extract discrete values from continuous signal

– Simplest version: 1-bit signal• Either high range (1) or low range (0)• With guard range between them

– Not strongly affected by noise or low quality circuit elements

• Can make circuits simple, small, and fast

Voltage

Time

0 1 0

HCL (hardware control language)

HCLHCL- - A programming language used to develop and understand the control logic of processor architecture.- - Describes the control logic of different processor design.

Logic Gate Types Logic Gate Types -- Logic gates are always active- Input → ... time → output

Voltage

Time

a

ba && b

Rising Delay Falling Delay

Combinational Circuits and HCL

Combinational circuitCombinational circuit- - Combination of logic gates- Output cannot be connected together- Acyclic

Combinational circuit to test for bit equalityCombinational circuit to test for bit equality- The output will equal 1 when both inputs are 0, or both are 1.

HCL code : Bool eq = (a && b) || (!a && !b)

Combinational Circuits and HCL

MultiplexorMultiplexor- Sets a value depending on a control input signal- The output will equal a when s is 1, and b when s is 0.

HCL code : Bool out = (s && a) || (!s && b)

Combinational Circuits and HCL

HCL versus CHCL versus C- Change occurs over time- There is no real assignment, just assignment to expressions- Expressions cannot be partially evaluated

Example:(a && !a) && func(b,c)

Combinational Circuits and HCL

Word-level equality test circuitWord-level equality test circuit

HCL code : Bool EQ = ( A == B)

Combinational Circuits and HCL

Word-level multiplexorWord-level multiplexorHCL (case expression) - 1 stands for default

Combinational Circuits and HCLMux 4Mux 4

int Out4 = [ !s1 && !s0 : A; !s1 : B; s1 && !s0 : C; 1 : D;];

Min 3Min 3

int Min3 = [ A <= B && A <= C : A; B <= A && B <= C : B; 1 : C;];

Arithmetic Logic Unit

 An arithmetic and logic unit (ALU) is a digital circuit that performs arithmetic and logical operations. The ALU is a fundamental building block of the Central Processing Unit of a computer, and even the simplest microprocessors contain one for purposes such as maintaining timers. The processors found inside modern CPUs and graphics processing units (GPUs) accommodate very powerful and very complex ALUs; a single component may contain a number of ALUs.

11

OFZFCF

OFZFCF

OFZFCF

OFZFCF

Arithmetic Logic Unit

Combinational logicContinuously responding to inputs

Control signal selects function computedCorresponding to 4 arithmetic/logical operations in Y86Addition, Subtraction, AND, OR

Also computes values for condition codes

A

L

U

Y

X

X + Y

0

A

L

U

Y

X

X - Y

1

A

L

U

Y

X

X & Y

2

A

L

U

Y

X

X ^ Y

3

A

B

A

B

A

B

A

B

The basic ALU provides the basic logical and arithmetic functions: AND, OR plus addition.

Shift, multiplication and division are usually outside the basic ALU.

Logical operations

1 bit logical unit for AND/OR operations

select (AND or OR)

result

0

1

MUX

a

b

Basic ALU (Combinational Circuit)

The ALU ALU includes combinational logic.

– Combinational logic a change in inputs directly causes a change in output, after a characteristic delay.

– Different from sequential logic which only changes on the clock.

Two major components of combinational logic are – multiplexors & decoders which we previously talked about.0

1

2

3

4

5

6

7

c

3 X 8 multiplexor

s1s2

0

1

2

3

4

5

6

7

DECODER

0

1

2

3 X 8 Decoder

s0

a b Cin sum Cout

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

inputs outputs

sum = (a b Cin) + (a b Cin) + (a b Cin)

+ (a b Cin) = a + b + Cin

Cout =(b Cin) + (a Cin) + (a b)

= ((a + b) Cin) + (a b)

a

b

Cout

Cin

Adder hardware for Cout

in 2 layers

1 bit FULL adder (3,2)

a b

CinCout

sum

Carry inCarry out

Full Adder from Half AddersHalf adder

Full adder from 2 half adders + or gate

a

b

Cout

sum

Cin

a

b

Cout

sum

1 bit simple ALU for logical / arithmetic operations - does not yet include subtraction.

a

b

select

result

0

1

2+

2

Cin

Cout

1 Bit Simple ALU

Enhanced for subtraction

a

b

select

result

0

1

2+

2

Cin

Cout

invert

1's complement

For subtraction use Cin = 1 and inverse b

subtraction: a + b + 1 = a + (b + 1) = a + (-b) = a - b

0

1

1 Bit Enhanced ALU

Ripple Carry Type Adder

To produce a 32 bit result, we connect 32 single bit units together.

This type of ALU adder is called a ripple adder

– Carry bits are generated in sequence.

– Bit 31 result and Cout is not correct until it receives Cin from previous unit, which is not correct until it receives Cin from its previous unit, etc.

– Total operation time is proportional to word size (here 32).

a0

b0result 0

Cin

Cout

Cin

ALU0

Cout

Cin

ALU1

Cout

Cin

ALU2

Cout

Cin

ALU31

Cout

.

.

.

a1

b1

a2

b2

a31

b31

result 1

result 2

result 31

.

.

.

operation = invert

+ select

32 bit ADDER with ripple carry:

3