ee321 chap01 review - univ-boumerdes.dz

EE321Computer Architecture

Chap 01 : Review of Digital DesignChap. 01 : Review of Digital Design

Dr. Abdelhakim KhouasEmail : [email protected]

ab khouas@univ boumerdes [email protected] (ex. INELEC)

University M’hamed Bougara of Boumerdes

Course chapters

1. Review of Digital Design2 T L l f C t2. Top Level of Computer3. Central Processing Unit (CPU)4. Control Unit5. Memory5. Memory6. Instruction Set and Addressing Modes7 Input/Output Devices7. Input/Output Devices

EE321 - Chap. 01 – Review © A. Khouas1

Lecture Outline

1 Di it l t1. Digital systems2. Binary representations3. Combinational logic circuits4. Sequential circuits4. Sequential circuits5. Logic families


1. Digital Systems

What is Digital Circuit (Logic Circuit)?a g a u ( og u )To solve some everyday problems, we use electronic circuitselectronic circuits.Two large groups of electronic circuits:

1. Analog circuits: continues-valued signals2. Digital (logic) circuits: discrete-values signalg ( g ) g

Word is analog, we use DAC and ADC to convert analog and digital signals


1. Digital Systems

Different designs to solve the sameDifferent designs to solve the same problem:1. Software design: We write a program1. Software design: We write a program

than can be executed by a processor (uprocessor, ucontroller, DSP, GPU, ... etc )etc.)

2. Hardware Design: We design electronic circuit

1 P i t d Ci it B d (PCB)1. Printed-Circuit Board (PCB)2. Application Specific Integrated Circuit (ASIC or

IC)3 P bl L i D i (PLD CPLD3. Programmable Logic Devices (PLD, CPLD,

FPGA, ...)3. Hardware/Software Design


Copyright @ 2005 Intel Corporation.

1. Digital Systems

Why Digital Circuit?1 Easy to design1. Easy to design2. High performances3 R b t t i3. Robustness to noise4. Low cost5.66.7.


1. Digital Systems

Bits and BytesIn digital systems we use a two-level logic component called a bit to represent digital signalcomponent called a bit to represent digital signal

One bit can take two logic values: ‘0’ and ‘1’ or High (H) and Low (L)and Low (L)


1. Digital Systems

Bits and BytesBits and BytesA group of bit is called bit-vectorLeftmost bit is referred to as MSB (Most Significant Bit)g )Rightmost is LSB (Least Significant Bit)A group of 8 bits (10011101) is called ByteA group of 8 bits (10011101) is called Byte1 Kbyte = 1024 Bytes = 8192 bits1 Mbyte = 1024 Kbyte = 1048576 Bytes1 Gbyte = 1024 Mbyte

EE321 - Chap. 01 – Review © A. Khouas

y y

7

1. Digital Systems

Logic value vs. Physical valueLogic values ‘L’ and ‘H’ are represented in the realLogic values L and H are represented in the real circuit by physical valuesIn fact the physical values for ‘L’ and ‘H’ areIn fact, the physical values for L and H are ranges of values

VOH: minimum output voltage for HighVOH: minimum output voltage for HighVOL: maximum output voltage for LowVIH i i i t lt t d t b Hi hVIH : minimum input voltage guaranteed to be HighVIL : maximum input voltage guaranteed to be Low


1. Digital Systems

Logic value vs. Physical valueLogic value vs. Physical valueOH = [VOH,VDD]OL= [0 , VOL]IH = [VIH,VDD]IL = [0,VIL]

Example: 5V HCMOS

VOL 0 26 VVOL = 0.26 VVOH = 4.48 VVIL = 1VVIH = 3.5VNoise Margin L = 0.74Noise Margin H = 0.96V


g

9

Source: Digital Design Principles and practices, by J. F. Wakerly

1. Digital SystemsComparison of logic levels of some technologies



2. Binary Representation

Positional Number SystemsyIn positional number system, each position has a weight based on powers of the base (e.g. 57 = 5 10 7)5x10+7)

Base 2k

1101 = 1+0+4+8 = 13

1 1 0 20

... *2 ik k i i

i

N a a a a a avec 0 a 1−=

= = ≤ ≤∑1101 1+0+4+8 13

Hexadecimal Numbers (base 16)Bits are grouped by 4Bits are grouped by 4 Hex is used just to simplify Human-system communication


co u ca o

11


Conversion: Decimal --> Base 2Conversion: Decimal > Base 2Division successives par 2

53 21 26 2

0 13 2

End of divisionsLSB

1 6 20 3 2

1 1 25310 = 1101012

Conversion: Base 2 -->Decimal

1 1 21 0MSB

Multiplication by power of 211012 = 1*20 + 0*21 + 1*22 + 1*23 = 1+4+8 = 1316


2 16

12


carry

1 1 11 1

1 1 1 0

1

1 4

+ 0 1 1 1

1 0 1 0 1

+ 7

2 11 0 1 0 1 2 1

Decimal Addition Binary Addition

Binary addition


y


5 1 0 1

x 6 x 1 1 0

0 0 0 0 * 101

+ 1 0 1 .

+ 1 0 1

1* 101 + left shift

1* 101 + 2 left shifts

= 30

+ 1 0 1 . .

= 1 1 1 1 0

1* 101 + 2 left shifts

Binary multiplication


y p


In computers and digital systems, the number of bits used to store binary numbers is limitedbits used to store binary numbers is limited==> operation overflow occurs when the result is

t l t b t d b th li it d btoo large to be represented by the limited number of bits

Solution:In unsigned arithmetic the Carry bit generated at theIn unsigned arithmetic the Carry bit generated at the

MSB is used for overflow



Last carry indicate overflowLast carry indicate overflowCarry bit saved in

flag registers

1 1 1 1 11 0 1 1 1 0 0 1 1851 0 1 1 1 0 0 1 185

+ 0 1 1 0 1 0 0 0 + 104= 0 0 1 0 0 0 0 1 = 33 2890 0 0 0 0 0 33 89

Decimal addition 8-bit binary addition

8 bit unsigned binary addition with overflow


8-bit unsigned binary addition with overflow


Signed binary numbersSigned binary numbersSign-magnitude representation1’s complement representation2’s complement representationp pExcess 2n-1-1

Example: 4 bitExample: 4-bit (5)10 = (0101)sm = (0101)1’C = (0101)2’C = (1100)E7( )10 ( )sm ( )1 C ( )2 C ( )E7

(-5)10 = (1101)sm = (1010)1’C = (1101)2’C = (0010)E7=


(0010)E7

17


2’s complement is the preferred representation2 s complement is the preferred representation for arithmetic operations

We have:

1 0 0 0 (ignore MSB carry bit)Z + Z = 1...1

Z Z⇒ + +1 0...0 0 (ignore MSB carry bit)1

Z ZZ Z

⇒ + + = =

⇒ − = +

2’s complement numbers can be added by ordinary binary addition ignoring MSB carry bit



Signed binary addition using 2’s complementSigned binary addition using 2 s complement representation

Examples of 4 bit signed binary addition


Examples of 4-bit signed binary addition Source: Digital Design Principles and practices, by J. F. Wakerly


How to detect overflow in signed arithmetic gaddition?

Overflow can occur only with the addition of two numbers of same signIf overflow occur, the sign of the result is different from the sign of the numbers. Also overflow can be gdetected if the carry in and the carry out of the LSB bit are different



3. Combinational Logic Circuits

Combinational vs Sequential circuitsCombinational vs. Sequential circuitsCombinational circuits: output depends only on its

t i t ( l )present input (memoryless)

Sequential circuits: output depends on its present and previous inputs (depends on its state)p p ( p )



Each combinational circuit can be described as:Equation : sum of products product of sumsEquation : sum of products, product of sums, factorial formT th t blTruth tableLogic diagramBinary Decision DiagramTiming diagramTiming diagram…etc



Timing diagram of logic circuitTiming diagram of logic circuitIt shows how the circuit respond to a pattern of input signalsTrans., delay, ytr: rising delaytf: falling delaytf: falling delaytpHL: tpLH:


Electronics – Second Edition, Copyright © 2000 Prentice Hall, Inc.


d f lTiming diagram of logic circuitWhy propagation delays are important in digitalWhy propagation delays are important in digital design?

Glitch example: s = A and not(A)


Electronics – Second Edition, Copyright © 2000 Prentice Hall, Inc.


Basic logic gatesCircuits implementing basic functions are called

gates. Any digital function can be realized with the g y gfollowing gates:




Basic logic gatesBasic logic gates

NAND() NOT(AND ()) oNAND() NOT(AND ()) or AND() NOT (NAND ()) ?




Basic logic gates74LS00: Quad 2-inputs NAND gate74LS02: Quad 2-inputs NOR gateQ p g74LS04: Hex inverter74LS08: Quad 2 inputs AND gate74LS08: Quad 2 inputs AND gate74LS32: Quad 2 inputs OR gate74LS86: Quad 2 inputs XOR gate




Circuit synthesis and optimization usingCircuit synthesis and optimization using Karnaugh-map



Multiplexer/DemultiplexerMultiplexer/Demultiplexer

Connection diagram, truth table and equations of the dual 4-input


g , q pmultiplexer (74LS153)


Decoder/Encoder

Pin diagram and truth table of the 3-to-8 table of the 3 to 8 decoder (74LS138).Note 1: G2= G2A + G2B


G2= G2A + G2B


ffTristate buffer

Circuit diagram, function table and logic symbol of the CMOS 3-state b ff



buffer.


Tristate buffer

Pin diagram and function table of the 3-state octal buffer (74LS244)


Pin diagram and function table of the 3 state octal buffer (74LS244).


Binary addition: Half Adder (HA)



Binary addition: Full Adder (FA)y ( )Sum = A xor B xor CinC t AB Ci B Ci ACout = AB+CinB+CinA

= AB+Cin(AxorB)

Karnaugh-map for CoutKarnaugh map for CoutCin\AB 00 01 11 100 0 0 1 00 0 0 1 01 0 1 1 1



Binary addition: n-bit adder (Ripple-carry Adder)



Binary addition: n bit adder/subtractorBinary addition: n-bit adder/subtractor



Arithmetic and logic unit (ALU)Arithmetic and logic unit (ALU)


4. Sequential Circuits

LatchD Clk Q+ Qn+

X 0 Q Qn

0 1 0 1

1 1 1 0

Memorisation Update

SClk

QnQ



Logic and pin diagram and function table of the quad latch (74LS75)


of the quad latch (74LS75).


Logic diagram and function table of the octal transparent latch with 3-state poutputs (74LS373).



D-type Flip-Flop (DFF)

S b l

D Clk Q+

Symbol

X 0 Q

X 1 Q

0 0

Master-slave positive-edgetriggered DFF

0 0

1 1

Function tableP iti d


Function tablePositive edge


D-type Flip-Flop (DFF)

S b l

D Clk Q+

Symbol

X 0 Q

X 1 Q

0 00 0

1 1

Function tablePositive-edge triggered DFF designed using


Function tableNAND gates

4. Sequential CircuitstHtSU

Setup time Hold timeSetup time Hold time

D

Clk

D

Q

D should be stable here

l d h

tPD

Setup time, hold time, and propagation delay for positive edge

Output is valide herePropagation delay


p , , p p g y f p gtriggered DFF


D t Fli Fl (DFF)D-type Flip-Flop (DFF)Equation: Q = D q QTableTiming diagram?Timing diagram?

DFF with enable signalgQ = D when En=1Table?Table?Timing diagram?



DFF ith bl d h t i lDFF with enable and asynchronous reset signalsEquation? qTable?Timing diagram?Timing diagram?

DFF with enable and synchronous set signalsy gEquation?Table?Table?Timing diagram?



Pin diagram and function table of the Dual Positive-Edge-Triggered DFF with Preset, Clear and Complementary Outputs (74LS74)


Preset, Clear and Complementary Outputs (74LS74).


Logic and pin diagram and function table of the octal


Logic and pin diagram and function table of the octal transparent DFF with 3-state outputs (74LS374).


N-bit Register :E quationsN bit Register Inputs : D(n-1:0) 0 0

:( ) ( )( ) ( )

E quationsQ t D tQ t D t

+ =

Output: Q[n-1:0]Symbol?

1 1

2 2

( ) ( )( ) ( )

Q t D tQ t D t

+ =+ =

yTiming Diagram? 3 3( ) ( )Q t D t+ =



Shift RegisterShift Register

0 1

:( 1) ( )( 1) ( )

E quationsQ t Q tQ t Q t

+ =

+ =

CLK D Q3 Q2 Q1 Q0

0 1 U U U U

1 0 1 U U U

1 2

2 3

3

( 1) ( )( 1) ( )( 1) ( )

Q t Q tQ t Q tQ t D t

+ =+ =+ =

2 0 0 1 U U

3 1 0 0 1 U

4 0 1 0 0 1


3 ( ) ( )Q5 0 0 1 0 0


CounterQ2 Q1 Q0 Q2+ Q1+ Q0+

Counter 0 0 0 0 0 1

0 0 1 0 1 0

0 1 0 0 1 1

0 1 1 1 0 0

1 0 0 1 0 1

1 0 1 1 1 01 0 1 1 1 0

1 1 0 1 1 1

1 1 1 0 0 0

:

( 1) ( )

Equations

Q t Q t+0 0

1 0 1

( 1) ( )( 1) ( ) ( )( 1) ( ) ( ) ( )

Q t Q tQ t Q t Q tQ t Q t Q t Q t

+ =+ = ⊕

+ = ⊕


2 0 1 2( 1) ( ). ( ) ( )Q t Q t Q t Q t+ = ⊕

5. Logic Families

TTL (Transistor-Transistor Logic) family( g ) yBased on Bipolar transistorReplaced by CMOS family in 1990Replaced by CMOS family in 1990

CMOSBased on MOSFET (Metal-Oxide Semiconductor Field Effect Transistor)Field Effect Transistor)


5. Logic Families

N-Channel MOS TransistorIf V 0 NMOS i OFFIf VGS=0, NMOS is OFFIf VGS=VDD, NMOS is ON

P Channel MOS TransistorP-Channel MOS TransistorIf VSG=0, PMOS is OFFSG

If VSG=VDD, PMOS is ON


5. Logic Families

CMOS InverterCMOS Inverter



5. Logic Families

CMOS 2-input NAND gateCMOS 2 input NAND gate



5. Logic Families

CMOS 2-input NOR gateCMOS 2 input NOR gate



5. Logic Families

CMOS GatesCMOS GatesWhat about AND and OR gates?


5. Logic Families

Other CMOS GatesOther CMOS GatesY = not(AB+C) ?

Y = A(B+C) ?Y = A(B+C) ?


Summary

Digital systemsDigital systemsAnalog vs digital systemsHardware vs software designHardware vs. software design

Binary representationsTwo’s complement representationTwo s complement representation

Combinational logic circuitsSeq ential ci c itsSequential circuitsLogic families

NMOS and PMOS transistorsCMOS Family


ee321 chap01 review - univ-boumerdes.dz

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