Lecture 3: Logic circuit

Combinational circuit and sequential circuit

TRAN THI HONG

HONG＠ IS.NAIST.JP

Content

Lecture 1: Computer organization and performance evaluation metrics

Lecture 2: Processor architecture and memory system

Lecture 3: Logic circuit: Combinational circuit and sequential circuit

Lecture 4: Number system and Its Importance

Lecture 5: Hardware design by HDL

Lecture 6: Parallel programming

Lecture 7: Hardware design by high-level synthesis

Lecture 8: Computer system design and its applications

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Lecture Information

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Grading (評価)Mini-test (40%) Score is based on the number of times that you attend the class and your

enthusiastic on doing mini-test.

You may get MAX score although your answer is not correct!

If you cannot attend the lecture with reasonable reason (ex: attend conference), you can get MAX score if you: Inform about your absent to me via email: hong@is.naist.jp

Study from lecture video and submit mini-test by next time.

Home-work: (60%) Score is based on the correction of your home-work

Bonus (+10%) Your activeness, enthusiastic during the lecture (make question, answer the question,

etc.)

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Basic Logic Circuits

Basic Logic Gates: Not, And, Or, Xor, Xnor, etc.

Combinational Circuits

Arithmetic Operator: adder, multiplier, etc.

Encoder

Multiplexer

Comparators

Sequential Circuits

Memory Elements: Latch, FlipFlop, Register, etc.

Sequential Circuits

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6

brick

7

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Overview of Hardware Circuit Design

Block

1

Binary Logic gate:

Not, And, Or, etc.

Transistors

System Block

2

Block

N…

Comb. Circuit: Do specific

function.

Seq. Circuit: Register,

memory, etc.

Adder Mul.

MUX Comp.

Latch Flipflop

Comparator

Adder Register Memory

Hardware System

Analog

Circuit

Design

Digital

Circuit

Design

Verilog HDL

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Transistor There are several types of transistor such as:

Bipolar junction transistor (BJT)

Field-Effect Transistor (FET)

Junction gate FET (JFET)

Metal-Oxide Semiconductor (MOS)

MOSFET

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Basic Logic GatesNOT Gate

Logic gates are the element building blocks of a digital circuit.

Basic element of logic gate is transistor

NOT gate is built from 2 MOS transistors

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Symbol

True-Table

0 1

1 0

Circuit

NOR gate is built from 4 transistors: 2 p-type in serial and 2 n-type in parallel

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Basic Logic GatesNOR Gate

01

0

10

1

Circuit

Symbol

True-Table

OR gate is built by adding a NOT gate into NOR gate

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Basic Logic GatesOR Gate

NOR

NOT

00

0

11

1

Symbol

True-Table

Circuit

NAND gate is built from 4 transistors: 2 p-type in parallel & 2 n-type in serial

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Basic Logic GatesNAND Gate

Circuit

Symbol

True-Table

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Basic Logic GatesAND Gate

NAND

NOT

Symbol

True-Table

Circuit

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Basic Logic GatesXOR Gate

Symbol

True-Table

Circuit

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Basic Logic GatesXNOR Gate

Symbol

True-Table

Circuit

Minitest-3.1How many p-type, n-type CMOS transistors are needed for building:

NAND gate

OR gate

XOR gate

XNOR gate

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Minitest-3.1: Answer How many p-type, n-type CMOS transistors are needed for building:

NAND gate: 2 p-type + 2 n-type CMOS transistors

OR gate: 3 p-type + 3 n-type CMOS transistors

XOR gate: 4 NOT + 2 NAND + 1 OR = 4 (1p + 1n) + 2 (2p + 2n) + 1 (3p + 3n) = 11 p-type + 11 n-type transistors

XNOR gate: 11 p-type + 11 n-type transistors

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Basic Logic Circuits

Basic Logic Gates: Not, And, Or, Xor, Xnor, etc.

Combinational Circuits

Arithmetic Operator: adder, multiplier, etc.

Encoder

Multiplexer

Comparators

Sequential Circuits

Memory Elements: Latch, FlipFlop, Register, etc.

Sequential Circuits

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Combinational Circuits- Arithmetic Circuits - (1/4)

Basic operator: adder

Subtractor is the adder of negative number.

Multiplier is the sum of multiple adders

Divider is very complex and rarely used in hardware design.

Half Adder

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Full Adder

Input Output

Combinational Circuits- Arithmetic Circuits - (2/4)

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A0 B0 A1 B1 A2 B2 A3 B3

S0 S1 S2 S3 C3

Half

Adder

Full

Adder

Full

Adder

Full

Adder

C0 C1 C2

4-bit Adder

Example:

1 1 0 1 (-3)

+ 0 1 1 0 (6)

1 0 0 1 1 (3)

A3 A2 A1 A0

+ B3 B2 B1 B0C3 C2 C1 C0

S3 S2 S1 S0

Combinational Circuits- Arithmetic Circuits - (3/4)

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Multiplier

Example:

010 (2)

× 101 (5)

010

+ 000

+ 010

01010 (10)

A2 A1 A0

×B2 B1 B0

A2 A1 A0 ×B0 ×1

+ A2 A1 A0 × B1 ×2

+ A2 A1 A0 × B2 ×4

A2×B0

A1×B0

A0×B0

A2×B1

A1×B1

A0×B1

A2×B2

A1×B2

A0×B2

A×B0

A×B1

A×B2

P0P1P2P3P4

Combinational Circuits- Arithmetic Circuits - (3/4)

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Other Combinational Circuits- Decoder -

- An n-to-2n decoder is a multiple output combinational logic circuit with n input and 2n output signals.

- For each possible input condition, one and only one output signal is active.

n-to2n

Decoder

… …

x0

x1

xn-1

LSB

MSB

m0

m1

mB

(B = 2n-1)

Exercise: Design a 2-to-4 decoder

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Input

x1 x0

Output

m3 m2 m1 m0

0 0 0 0 0 1

0 1 0 0 1 0

1 0 0 1 0 0

1 1 1 0 0 0

- Multiplexer (or MUX) selects one of many input signals to appear on a single output line

- Demultiplexer (or DEMUX) takes a single input signals and routes it to one of several output signals.

Other Combinational Circuits- Multiplexer & Demultiplexer -

D0

D1

Dn

Y

D0

D1

Dn

Y

MUX DEMUX

SEL

D0

Dn

Y Y

SEL

D0

Dn

… ………

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- A comparator determines the relative magnitude of two binary numbers.

- There are many types of comparators such as:

Other Combinational Circuits- Comparator-

>A

BY1 <

A

BY2

≥A

BY3 ≤

A

BY4

=A

BY5

Input

Relationship

Output

Y1 Y2 Y3 Y4 Y5

A > B 1 0 1 0 0

A < B 0 1 0 1 0

A = B 0 0 1 1 1

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Combinational Circuits

Combinational circuit: used for calculation

◦ Always representing a present state

◦ No past state in the circuit

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A

NOT gate

out = A

out

NAND gate

A

Bout = AB

out

XOR gate

A

B out = A^B

out

“Out” changes

when A or B changes;

No past, nor next info.

Combinational Circuits

Combinational Circuits

◦ Always represent a current state

◦ No past state in the circuit

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Not possible to achieve “counter”

Counter:

◦ 0123… N

+ 1A A_plus1

Comb. Logic

Q: What will happen on A_plus1?

A: A_plus1 will go ∞ w/o stop!

No stable state if input is not stable.

That’s the reason we need sequential circuit.

Minitest-3.2

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0

1

1

0

= 2’b10

?

?

?

?

??

??

?

?

?

?

?

Minitest-3.2: Answer

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0

1

1

0

= 2’b10

0

0

1

0

11

00

0

0

1

0

1

0 0 1 0 SEL = 2’b10 = 2

Y = D2

Basic Logic Circuits

Basic Logic Gates: Not, And, Or, Xor, Xnor, etc.

Combinational Circuits

Arithmetic Operator: adder, multiplier, etc.

Encoder

Multiplexer

Comparators

Sequential Circuits

Memory Elements: Latch, FlipFlop, Register, etc.

Sequential Circuits

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- Sequential circuit is a circuit that is able to REMEMBER its previous data.

- Two main types:

Latch

FlipFlop

Latch FlipFlop

Controlled by excitation input

signals

Controlled by clock signal

Two types:

- Set latch: force to 1

- Reset latch: force to 0

Many Types:

- Master Slave SR FlipFlop

- Master Slave D FlipFlop

- Master Slave JK FlipFlop

- Edge-triggered D FlipFlop

- Edge-triggered JK FlipFlop

- T FlipFlop

Device state is changed

immediately

Device state is changed after 1

clock cycle

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Memory Elements

Memory ElementsSR Latch

Set Reset Latch◦ “Set” means “output 1”

◦ “Reset” means “output 0”

e.g. reset status◦ The feedback loop creates stable status

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S R Q Q’

0 0 Qprev Q’prev (stored)

0 1 0 1 (reset)

1 0 1 0 (set)

1 1 0 0 (not used)

S

RQ

Q’

0

1

1

0

0

1

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E D Q Q’

0 x Qprev Q’prev (stored)

1 0 0 1 (reset)

1 1 1 0 (set)

Memory ElementsGate D Latch

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D

cp=0

Q

Accept input Keep (Locked)

cp

cp

D

cp=1

Q

Keep (Locked) Accept input

Memory ElementsMaster/Slave D FlipFlop

Register

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Enable

Clock

Data in

Data outbmsb ... b1 b0

bmsb ... b1 b0

bmsb ... b1 b0

bmsb ... b1 b0

…

Clock

Write_address

read_address

Write_data

Write_enable

read_data

Memory: is a bank of registers

Memory ElementsMaster/Slave D FlipFlop

Sequential Logic CircuitsDefinition: Outputs depends on stored information (current state) and current inputs

◦ Example: Bank account

◦ State = Waiting for new operation (stored value: your current balance)

◦ Input = Withdraw or deposit

◦ Output = Your new balance

Combinational logic and one/or more memory elements are used in sequential logic

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input output

Mem. Element

Comb.

Logic

Sequential Circuit

Memory element

◦ Provide a lock of current status

Combinational logic

◦ Calculate new status

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input output

Mem. Element

Comb.

Logic

Sequential Circuit

Sequential Logic Circuits

Modeling the Circuit

Looking into the memory

◦ It stores n-bits

◦ 1 bit has two states, as 0 and 1;

◦ 2 bits have four states, as 00, 01, 10, 11;

◦ n bits have 2n states.

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input output

Comb.Logic

Sequential Circuit

Mem. Element

The amount of information to be stored is “finite”

◦ a Finite State Machine (FSM) to describe the 2n states

Two Kinds of FSM Models

Mealy Machine

◦ Outputs are function of the present/current state and the present inputs

Moore Machine

◦ Outputs are independent of the inputs i.e. dependent on present state only

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input output

Comb.Logic

Sequential Circuit

Mem. Element

input output

Comb.Logic

Sequential Circuit

Mem. Element

Major FSM model we use

Minitest-3.3

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1

1

?

?

?

?

Minitest-3.3: Answer

42

1

1

?

?

?

?

1

1

0

1

1

0

Summary

Basic Logic Gates: Not, And, Or, Xor, Xnor, etc.

Combinational Circuits

Arithmetic Operator: adder, multiplier, etc.

Encoder

Multiplexer

Comparators

Sequential Circuits

Memory Elements: Latch, FlipFlop, Register, etc.

Sequential Circuits

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