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Processor Architecture Logic Design. David O’Hallaron. Carnegie Mellon University. http:// mprc.pku.edu.cn / ics /. Overview of Logic Design. Fundamental Hardware Requirements Communication How to get values from one place to another Computation Storage Bits are Our Friends

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Processor Architecture

Logic Design

David O’Hallaron

Carnegie Mellon University

http://mprc.pku.edu.cn/ics/

overview of logic design
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

0

1

0

Voltage

Time

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
computing with logic gates

a && b

Computing with Logic Gates
  • Outputs are Boolean functions of inputs
  • Respond continuously to changes in inputs
    • With some, small delay

Falling Delay

Rising Delay

b

Voltage

a

Time

combinational circuits

Acyclic Network

Primary

Inputs

Primary

Outputs

Combinational Circuits
  • Acyclic Network of Logic Gates
    • Continously responds to changes on primary inputs
    • Primary outputs become (after some delay) Boolean functions of primary inputs
bit equality

Bit equal

a

eq

b

Bit Equality
    • Generate 1 if a and b are equal
  • Hardware Control Language (HCL)
    • Very simple hardware description language
      • Boolean operations have syntax similar to C logical operations
    • We’ll use it to describe control logic for processors

HCL Expression

bool eq = (a&&b)||(!a&&!b)

word equality

b31

Bit equal

eq31

a31

b30

Bit equal

eq30

a30

Eq

B

=

Eq

b1

Bit equal

eq1

A

a1

b0

Bit equal

eq0

a0

Word Equality

Word-Level Representation

  • 32-bit word size
  • HCL representation
    • Equality operation
    • Generates Boolean value

HCL Representation

bool Eq = (A == B)

bit level multiplexor
Bit-Level Multiplexor
  • Control signal s
  • Data signals a and b
  • Output a when s=1, b when s=0

s

Bit MUX

HCL Expression

bool out = (s&&a)||(!s&&b)

b

out

a

word multiplexor

s

b31

out31

a31

s

b30

out30

MUX

B

Out

a30

A

b0

out0

a0

Word Multiplexor

Word-Level Representation

  • Select input word A or B depending on control signal s
  • HCL representation
    • Case expression
    • Series of test : value pairs
    • Output value for first successful test

HCL Representation

int Out = [

s : A;

1 : B;

];

hcl word level examples

MIN3

C

Min3

B

A

s1

s0

MUX4

D0

D1

Out4

D2

D3

HCL Word-Level Examples

Minimum of 3 Words

  • Find minimum of three input words
  • HCL case expression
  • Final case guarantees match

int Min3 = [

A < B && A < C : A;

B < A && B < C : B;

1 : C;

];

4-Way Multiplexor

  • Select one of 4 inputs based on two control bits
  • HCL case expression
  • Simplify tests by assuming sequential matching

int Out4 = [

!s1&&!s0: D0;

!s1 : D1;

!s0 : D2;

1 : D3;

];

arithmetic logic unit

2

1

0

3

Y

Y

Y

Y

A

A

A

A

X ^ Y

X & Y

X + Y

X - Y

X

X

X

X

B

B

B

B

OF

OF

OF

OF

ZF

ZF

ZF

ZF

CF

CF

CF

CF

A

L

U

A

L

U

A

L

U

A

L

U

Arithmetic Logic Unit
  • Combinational logic
    • Continuously responding to inputs
  • Control signal selects function computed
    • Corresponding to 4 arithmetic/logical operations in Y86
  • Also computes values for condition codes
storing 1 bit

V2

q

Q+

!q

Q–

Vin

V1

q = 0 or 1

Storing 1 Bit

Bistable Element

storing 1 bit cont

V2

q

Q+

!q

Q–

Vin

V1

Stable 1

q = 0 or 1

Vin = V2

V2

Vin

V1

Metastable

Stable 0

Storing 1 Bit (cont.)

Bistable Element

physical analogy

Stable 1

.

.

.

Metastable

Stable 0

Physical Analogy

Metastable

Stable left

Stable right

storing and accessing 1 bit

Bistable Element

R-S Latch

q

Q+

R

Q+

!q

Q–

Q–

q = 0 or 1

S

Resetting

Setting

Storing

1

0

0

1

0

!q

0

1

q

1

0

!q

0

1

q

0

1

0

Storing and Accessing 1 Bit
1 bit latch

D

R

Q+

Q–

C

S

Latching

Storing

d

!d

!d

!d

d

d

!d

0

!q

q

1

0

!q

q

d

d

!d

0

1-Bit Latch

D Latch

Data

Clock

transparent 1 bit latch

Changing D

Time

Latching

C

d

!d

!d

!d

d

D

Q+

1

d

d

!d

Transparent 1-Bit Latch
  • When in latching mode, combinational propogation from D to Q+ and Q–
  • Value latched depends on value of D as C falls
edge triggered latch

C

T

D

Q+

Time

Edge-Triggered Latch
  • Only in latching mode for brief period
    • Rising clock edge
  • Value latched depends on data as clock rises
  • Output remains stable at all other times

D

R

Data

Q+

Q–

C

S

T

Clock

Trigger

registers

i7

D

o7

Q+

C

i6

D

o6

Q+

C

i5

D

o5

Q+

C

i4

D

o4

Q+

I

O

C

i3

D

o3

Q+

C

i2

D

o2

Q+

C

i1

Clock

D

o1

Q+

C

i0

D

o0

Q+

C

Clock

Registers

Structure

  • Stores word of data
    • Different from program registers seen in assembly code
  • Collection of edge-triggered latches
  • Loads input on rising edge of clock
register operation

Rising

clock

State = y

y

Output = y

Register Operation
  • Stores data bits
  • For most of time acts as barrier between input and output
  • As clock rises, loads input

State = x

x

Input = y

Output = x

state machine example

Comb. Logic

0

MUX

0

Out

In

1

Load

Clock

Clock

Load

A

L

U

x0

x1

x2

x3

x4

x5

In

x0

x0+x1

x0+x1+x2

x3

x3+x4

x3+x4+x5

Out

State Machine Example
  • Accumulator circuit
  • Load or accumulate on each cycle
random access memory

valA

Register

file

srcA

A

valW

Read ports

W

dstW

Write port

valB

srcB

B

Clock

Random-Access Memory
  • Stores multiple words of memory
    • Address input specifies which word to read or write
  • Register file
    • Holds values of program registers
    • %eax, %esp, etc.
    • Register identifier serves as address
      • ID 15 (0xF) implies no read or write performed
  • Multiple Ports
    • Can read and/or write multiple words in one cycle
      • Each has separate address and data input/output
register file timing

Register

file

Register

file

y

2

valW

valW

W

W

dstW

dstW

x

valA

Register

file

srcA

A

2

Clock

Clock

valB

srcB

B

x

2

Rising

clock

y

2

Register File Timing
  • Reading
    • Like combinational logic
    • Output data generated based on input address
      • After some delay
  • Writing
    • Like register
    • Update only as clock rises

x

2

hardware control language
Hardware Control Language
    • Very simple hardware description language
    • Can only express limited aspects of hardware operation
      • Parts we want to explore and modify
  • Data Types
    • bool: Boolean
      • a, b, c, …
    • int: words
      • A, B, C, …
      • Does not specify word size---bytes, 32-bit words, …
  • Statements
    • bool a = bool-expr ;
    • int A = int-expr ;
hcl operations
HCL Operations
    • Classify by type of value returned
  • Boolean Expressions
    • Logic Operations
      • a && b, a || b, !a
    • Word Comparisons
      • A == B, A != B, A < B, A <= B, A >= B, A > B
    • Set Membership
      • A in { B, C, D }
        • Same as A == B || A == C || A == D
  • Word Expressions
    • Case expressions
      • [ a : A; b : B; c : C ]
      • Evaluate test expressions a, b, c, … in sequence
      • Return word expression A, B, C, … for first successful test
summary
Summary
  • Computation
    • Performed by combinational logic
    • Computes Boolean functions
    • Continuously reacts to input changes
  • Storage
    • Registers
      • Hold single words
      • Loaded as clock rises
    • Random-access memories
      • Hold multiple words
      • Possible multiple read or write ports
      • Read word when address input changes
      • Write word as clock rises
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