Basic logical operations

2.2.3 Operation Mechanism

Through the combination of circuits that perform these three operations, a wide range of logical circuits is implemented.

Logical product operation (AND operation)

Logical sum operation (OR operation)

Negation operation (NOT operation)

Basic logical operations

Logical sum (OR)

Logical product (AND)

Logical operations Operation symbols

Negation (NOT)

Exclusive logical sum (EOR)

Negative logical sum (NOR)

Negative logical product (NAND)

^ ∙V +¯ ¬

Logical Circuits

Basic Circuits and their Combination

AND circuit

OR circuit

NOT circuit

EOR circuit

NOR circuit

NAND circuit

Combinational Circuit

Identity circuitAddition circuit

Half adder circuit

Full adder circuit

Sequential Circuit

Flip-flop circuit

AND circuit of a switch and a light bulb

AND circuit

Basic logical circuits

2.2.3 Operation Mechanism

Truth Table

A B A AND B

0 0 0

0 1 0

1 0 0

1 1 1

Venn Diagram A^B (or A B)∙

switch A

switch B

switch A switch B

open (0) open (0)

open (0) close (1)

close (1) open (0)

close (1) close (1)

A: 0 B: 0 A ^ B = 0

A: 0 B: 1 A ^ B = 0

A: 1 B: 0 A ^ B = 0

A: 1 B: 1 A ^ B = 1

AB

Y

MIL –STDUS Military standard

AND symbol

OR circuit of a switch and a light bulb

OR circuit

Basic logical circuits

2.2.3 Operation Mechanism

Truth Table

A B A OR B

0 0 0

0 1 1

1 0 1

1 1 1

Venn Diagram AνB (or A+B)A B

AB

Y

MIL –STDUS Military standard

OR symbol

NOT circuit of a switch and a light bulb

NOT circuit

Basic logical circuits

2.2.3 Operation Mechanism

Truth Table

A NOT A

0 1

1 0

A

Venn Diagram ¬AA

A Y

MIL –STDUS Military standard

NOT symbol

EOR, NOR & NAND circuits

Combination of the basic circuits

2.2.3 Operation Mechanism

Truth Tables

A B A EOR B

0 0 0

0 1 1

1 0 1

1 1 0

A B A NOR B

0 0 1

0 1 0

1 0 0

1 1 0

A B A NAND B

0 0 1

0 1 1

1 0 1

1 1 0

AB

Y

MIL –STDUS Military standard

EOR symbol

AB

Y

NOR symbol

AB

Y

NAND symbol

Exclusive logical sum operation circuit

Negative logical sum operation circuit

Negative logical product operation circuit

Addition circuits

Combination of the basic circuits

2.2.3 Operation Mechanism

Truth Table

Input Output

A B C D

0 0 0 0

0 1 0 1

1 0 0 1

1 1 1 0

Half-adder circuit

Addition of two 1-digit nos.

a+ b──c d

Full-adder circuit

ac'

EOR circuit

AND circuit

EOR circuit

AND circuit

OR circuitb

Result d

Carry e

ab

EOR circuit

AND circuit

Result d

Carry c

Input Output

c’ a b e d

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

c'a

+ b──

e d

Sequential circuit

Combination of the basic circuits

2.2.3 Operation Mechanism

Sequential circuit

• a circuit in which the output is established according to the

current input and the status preserved (past input).

• status changes with time

• composed of a flip-flop circuit and is used in registers, etc.NOR circuit

NOR circuit

2.2.4 Multi-Processor

Multi-processor systems are introduced to improve the performance and reliability of the system.

Multiple processors are in parallel with each processor having a dedicated function.

When failure occurs, the processor will do a switch

and the remaining processors will distribute the load among themselves.

Symmetric Multi-Processor

2.2.4 Multi-Processor

Memory is shared among all the processors executing the same OS.

Competition for the use of memory among the processors since the memory common to all.

A large number of processors cannot be connected.

Message passing distributed memory multi processor systems

- systems where each processor has its own private block memory.

- a high speed I/O port is used to transfer the data between the different blocks.

Array Processor

2.2.4 Multi-Processor

The sub units’ acts are in a queue passing the result

to the next unit after it has finished its part (vector processing)

Mostly used in:

Supercomputers

High speed scientific computing

Large scale or dedicated mathematical processors

Parallel

2.2.4 Multi-Processor

Multiple processors cooperate with multiple tasks being performed to execute one job.

SISD (Single Instruction Single Data Stream)One Instruction stream operating on a single data element and is not parallel.

SIMD (Single Instruction Multiple Data Stream)Each instruction may operate on more than one data element and is synchronous.

Parallel SIMDThe same instruction is executed by all processors operating on different sets of data

MIMD (Multiple Instruction Multiple Data Stream)Each instruction has its own instruction stream and

acts on its own data stream independent of other processors.

MIPS (Million Instructions per Second)

2.2.5 Processor performance

Indicates, in million units, the number of instructions that can be executed in one second.

The higher the number of instructions that can be executed, the higher the value.

Mainly used to indicate the performance of processors of high-end mainframe computers.

However, it is meaningless to use this index to compare

processors of different types of machines that execute different instruction contents.

Clock

2.2.5 Processor performance

A processor has an internal clock to set the pace in which the micro-instructions, which are basic operations, are executed,

Uses a quartz crystal oscillator that pulses in regular intervals when electric current passes through.

The time taken for this oscillator to pulse once (one cycle) is called clock.

The basic operations of the processor are performed according to this clock.

The number of clocks vary according to the instruction.

Clock Frequency- clock reciprocal number- used as an index to measure the performance of a personal computer.

CPI (Cycles per Instruction)

2.2.5 Processor performance

A CPI is the number of clocks required to execute one instruction.

This index indirectly indicates the execution time of one instruction.