Course : AIT 204Course Title : Computer Organization and Architecture (COA)Course Credits : 3 + 0Course Teacher : Dr. Y R Ghodasara & Prof. K. C. Kamani

College of Agricultural Information Technology

Anand Agricultural UniversityAnand

Unit II

HALF ADDERA digital circuit that performs the arithmetic addition of two bits is called half adder.

1-bit addition

0+0--- 0

0+1---01

1+0---01

1+1---10

11-0

1Carry

A

B

CircuitA

B

Sum

Carry

Block Diagram of Half Adder

0 1

1 0

A B SUM CARRY

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

SUM

A B0 1

1

1

Rectangle 1A B0 1

R1=A’B

Rectangle 2A B1 0

R2=AB’

SUM = R1 + R2 = A’B+AB’

0 0

0 1

CARRYA B 0 1

1

1Rectangle 1

A B1 1

R1=ABA’BA

SUMB

B’AB’

A’

CARRY

Half Adder Circuit

FULL ADDERA digital circuit that performs the arithmetic addition of multiple bits is called a full adder.2-bit addition

00+10--- 10

10+10---100

11+01---100

11+11---110

11-0

11-1

1Carry

1Carry

A

B

CircuitA

B

Cin

Sum

Cout

Block Diagram of Full Adder

Full Adder

Cout

Sum

Cin

A

B

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

ENCODERA encoder is a digital circuit that converts binary information from the 2n input to n outputs.

Circuit N output…2N Inputs

Block Diagram of Encoder

4 X 2 ENCODER

Encoder

D1

4 X 2 Encoder

D4

D3D2

A

B

D1 D2 D3 D4

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

A B

0 0

0 1

1 0

1 1

D1

D4

D3D2

A

B

4 X 2 Encoder

CircuitN input … 2N Inputs

Block Diagram of Decoder

2 X 4 DECODER

DecoderD1

2 X 4 Decoder

D4

D3D2

A

B

DECODERA decoder is a digital circuit that converts binary information from the n coded input to maximum of 2n outputs.

2 X 4 Decoder

A

B D1

D4

D3

D2

A B D1 D2 D3 D4

0 0 1 0 0 0

0 1 0 1 0 0

1 0 0 0 1 0

1 1 0 0 0 1

MULTIPLEXER(MUX)A multiplexer is a digital circuit that receives binary information from one of 2n input data lines and directs it to a single output line.

4-to-1-line Multiplexer

S0

S1

I0

Y

S0 S1 Y

0 0 I0

0 1 I1

1 0 I2

1 1 I3

I1 I2 I3

DEMULTIPLEXER(DEMUX)A demultiplexer is a digital circuit which performs the opposite operation to the MUX. It functions as an electronic switch to route an incoming data signal to one of the several outputs.

1-to-4-line Demultiplexer

S0

S1Y0

D

Y1

Y2

Y3

D S0 S1 Y0 Y1 Y2 Y3

D 0 0 D 0 0 0

D 0 1 0 D 0 0

D 1 0 0 0 D 0

D 1 1 0 0 0 D

SEVEN SEGMENT DIGITAL CIRCUIT PROJECT

b

a

d

ceg

f

b

a

d

ceg

f

0010 a,b,d,e,g

b

a

ceg

fI1

I2

I3

I4

Digit Segments

0 abcdef

1 bc

2 abdeg

3 abcdg

4 bcfg

5 acdfg

6 acdefg

7 abc

8 abcdefg

9 abcdfg

b

a

d

ceg

f

Inputs Hex Value Segments

I1 I2 I3 I4 a b c d e f g

0 0 0 0 0 1 1 1 1 1 1 0

0 0 0 1 1 0 1 1 0 0 0 0

0 0 1 0 2 1 1 0 1 1 0 1

0 0 1 1 3 1 1 1 1 0 0 1

0 1 0 0 4 0 1 1 0 0 1 1

0 1 0 1 5 1 0 1 1 0 1 1

0 1 1 0 6 1 0 1 1 1 1 1

0 1 1 1 7 1 1 1 0 0 0 0

1 0 0 0 8 1 1 1 1 1 1 1

1 0 0 1 9 1 1 1 1 0 1 1

b

a

d

ceg

f

ClockIn many digital circuits the order in which events happen is critical. Sometimes one event must precede another, sometimes two events must occur simultaneously. To allow designers to achieve the required timing relations, many digital circuits use clocks to provide synchronization.A clock in this context is a circuit that emits a series of pulses with a precise pulse width and precise interval between consecutive pulses.The interval between corresponding edges of two consecutive pulses is called the clock cycle time.To achieve high accuracy, the clock frequency is usually controlled by a crystal oscillator.

Delay

C1

C2

Clock cycle

Crystal Oscillator

Flip FlopTo store 1-bit value we need a circuit that somehow “remembers” previous input values. This circuit is called flip-flop. There are variety of flip flops, all of which share two properties. • The flip flop is a bi-stable device. It exist in one of two states. In the absence of

input remains in that state. Thus a flip flop can function as a 1-bit memory.• The flip flop has two outputs, which are always the complements of each other.

These are generally labeled Q and Q’.• In electronics, a flip-flop or latch is a circuit that has two stable states and can be

used to store state information. Flip Flop is a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are a fundamental building block of digital electronics systems used in computers, communications, and many other types of systems.

• Flip-flops and latches are used as data storage elements. Such data storage can be used for storage of state, and such a circuit is described as sequential logic. When used in a finite-state machine, the output and next state depend not only on its current input, but also on its current state (and hence, previous inputs). It can also be used for counting of pulses, and for synchronizing variably-timed input signals to some reference timing signal.

• Flip-flops can be either simple (transparent or opaque) or clocked (synchronous or edge-triggered); the simple ones are commonly called latches.The word latch is mainly used for storage elements, while clocked devices are described as flip-flops.

SR Flip Flop [ SET RESET FLIP FLOP ]

S

RQ

Q’

0

0

1

01

0

The above circuit is known as SR Flip Flop.It has two inputs, S for Setting the flip flop and R for Resetting (Clearing) flip flop.It also has two outputs, Q and Q’ which are complementary.

If S=0 R=0 and Q=0 then First NOR gate output is 1(Q’) and Second NOR gate output is 0.If S=0 R=0 and Q=1 then First NOR gate output is 0(Q’) and Second NOR gate output is 1.

If S=1 R=0 and Q=0 then First NOR gate output is 0(Q’) and Second NOR gate output is 1(Q). (Set Operation)If S=0 R=1 and Q=1 then Second NOR gate output is 0(Q) and first NOR gate output is 1(Q’). (Reset Operation)

S R Q Q’0 0 Q Q’

1 0 1 0

0 1 0 1

1 1 - -

Clocked SR Flip Flop [ SET RESET FLIP FLOP ]

S

RQ

Q’

0

0

1

01

0

S R Clock Q Q’0 0 0 Q Q’

0 0 1 Q Q’

1 0 0 Q Q’

1 0 1 1 0

0 1 0 Q Q’

0 1 1 0 1

1 1 0 Q Q’

1 1 1 - -

S

R

Q’

Q

Ck

Clocked D Flip Flop [ DATA FLIP FLOP ]

D

Q

Q’

1

01

0

D Clock Q Q’0 0 Q Q’

0 1 0 1

1 0 Q Q’

1 1 1 0

One problem with SR Flip Flop is that the condition R=1 S=1 must be avoided.One way to do this is to allow just a single input.The D Flip Flop accomplish this.In D Flip Flop one input D is split into two inputs. One input is inverted using Inverter. Both inputs are given two AND gates.The D Flip Flop is also known as Data Flip Flop because it is used to store 1-bit data.

D Q’

Q

Ck

Clocked JK Flip Flop

J

Q

Q’

1

01

0K

J K Clock Q Q’0 0 0 Q Q’

0 0 1 0 1

1 0 0 Q Q’

1 0 1 1 0

0 1 0 Q Q’

0 1 1 0 1

1 1 0 Q Q’

1 1 1 1 0

One problem with SR Flip Flop is that the condition R=1 S=1 must be avoided.This problem is solved using JK Flip Flop.

J

K

Q’

Q

Ck

D Flip-Flop from NAND Latch• The output Q will track the input D so long as the flip-flop remains enabled.• A D flip-flop constructed from a NAND-latch .

Clocked D Flip Flop

Clocked J K Flip Flop using NAND Gates:

The J-K flip-flop is the most versatile of the basic flip-flops. It has the input- following character of the clocked D flip-flop but has two inputs,traditionally labeled J and K. If J and K are different then the output Q takes the value of J at the next clock edge. A simplified version of the versatile J-K flip-flop. Note that the outputs feed back to the enabling NAND gates. This is what gives the toggling action when J=K=1.

DefinitionsCombinational CircuitA combinational circuit is a connected arrangement of logic gates with set of inputs and outputs. At any given time, the binary values of the outputs are function of the binary combination of the inputs.

N inputs M outputs

Examples : Encoder, Decoder, Adder, Multiplexer, Demultiplexer

Sequential CircuitA sequential circuit is an interconnection of flip flops and gates. The gates by themselves constitute a combinational circuit, but when included with the flip flops, the overall circuit is classified as a sequential circuit.

Combinational Circuit

Flip Flops

Clock

Inputs Outputs

Examples : SR Flip Flop, D Flip Flop, JK Flip Flop

Integrated Circuit (IC/ IC Chip)Developed in the 1950s by Jack Kilby of Texas Instruments and Robert Noyce of Fairchild Semiconductor.

Gates are not manufactured or sold individually but rather in units called Integrated Circuits, often called ICs or chips.

• An IC is a square piece of silicon about 5 X 5 mm on which some gates have been deposited.• An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set

of electronic circuits on one small plate ("chip") of semiconductor material, normally silicon. This can be made much smaller than a discrete circuit made from independent components.

• Integrated circuits are used in virtually all electronic equipment today and have revolutionized the world of electronics. Computers, mobile phones, and other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the low cost of producing integrated circuits.

• ICs can be made very compact, having up to several billion transistors and other electronic components in an area the size of a fingernail. The width of each conducting line in a circuit (the line width) can be made smaller and smaller as the technology advances, in 2008 it dropped below 100 nanometers and in 2013 it is expected to be in the teens of nanometers

Chips can be divided into classes based on the number of gates they contain :• SSI Circuit (Small Scale Integration) : 1 to 10 gates• MSI Circuit (Medium Scale Integration) : 10 to 100 gates• LSI Circuit (Large Scale Integration) :100 to 1,00,000 gates

VLSI Circuit (Very Large Scale Integration) : > 1,00,000 gates• ULSI (Ultra large-scale integration): More than 1 million electronic components per chip • WSI• SoC• 3D IC

Wafer-scale integration (WSI) is a system of building very-large integrated circuits that uses an entire silicon wafer to produce a single "super-chip". Through a combination of large size and reduced packaging, WSI could lead to dramatically reduced costs for some systems, notably massively parallel supercomputers. The name is taken from the term Very-Large-Scale Integration, the current state of the art when WSI was being developed.

A system-on-a-chip (SoC or SOC) is an integrated circuit in which all the components needed for a computer or other system are included on a single chip. The design of such a device can be complex and costly, and building disparate components on a single piece of silicon may compromise the efficiency of some elements. However, these drawbacks are offset by lower manufacturing and assembly costs and by a greatly reduced power budget: because signals among the components are kept on-die, much less power is required (see Packaging).

A three-dimensional integrated circuit (3D-IC) has two or more layers of active electronic components that are integrated both vertically and horizontally into a single circuit. Communication between layers uses on-die signaling, so power consumption is much lower than in equivalent separate circuits. Judicious use of short vertical wires can substantially reduce overall wire length for faster operation.

4-bit Parallel Register

D Q’

Q

Ck

D Q’

Q

Ck

D Q’

Q

Ck

D Q’

Q

Ck

Clock

D1 D2 D3 D4

D5 D6 D7 D8

Input Lines

Output Lines

D1

D2

D3

D4

4-bit Shift Register

D Q’

Q

Ck

D Q’

Q

Ck

D Q’

Q

Ck

D Q’

Q

Ck

Clock

Serial In

Serial Out

Serial in