Theory of Computer Science Basic components of a computer Gate (logical Gate) Flip-flop Register...

Theory of Computer Science

Basic components of a computer

• Gate (logical Gate)

• Flip-flop

• Register

• Memory

• Arithmetic-Logic Unit -ALU

• Central Processing Unit - CPU

• Decoder and encoder

Theory of Computer Science - Basic components of a computer

Electronic parts (transistors, resistors) -> Gates

Gates -> Flip-flopGates -> Decoder and encoderGates + Flip-flops -> RegisterGates + Flip-flops -> MemoryGates + Flip-flops -> Arithmetic-Logic Unit - ALU

Registers + Memory + ALU + Bus connection ->Central Processing Unit - CPU

CPU + Memory + Input/Output devices -> computer


Central Processing Unit - CPU


Gates

Binary variable● Binary arithmetic is the basis notation in the computer technique● Binary variable have only 2 values called bits: 0 and 1

● The basic components of the computer realize the operations on single bit

● Basic Gates:● the negation NOT● the logical sum OR● the logical product AND● the negation of the sum NOR● the negation the products NAND● the sum modulo 2 XOR


The Gate of negation – NOT

● The logical function:

● The change of the entrance signal x on opposite


The Gate of logical sum OR

● The logical function: z = x + y

● Exit signal y equal 0 only when there are 0 on both entries

x y z

0 0

0 1

1 0

1 1


The Gate of logical sum OR

● The logical function: z = x + y



The Gate of logical product AND

● The logical function: z=xy


x y z

0 0

0 1

1 0

1 1


The Gate of logical product AND

● The logical function: z=xy



The Gate of negation of the sum NOR



x y z

0 0

0 1

1 0

1 1


The Gate of negation of the sum NOR




The Gate of negation the products NAND



x y z

0 0

0 1

1 0

1 1


The Gate of negation the products NAND




The Gate of sum modulo 2 XOR


● Exit signal y equal 1 only when there is one on exactly one entry

x y z

0 0

0 1

1 0

1 1


The Gate of sum modulo 2 XOR


● Exit signal y equal 1 only when there is one on exactly one entry


The de Morgan statement:

x y

0 0

0 1

1 0

1 1


The de Morgan statement:


The flip-flop

● The system having of 2 stable states (Q and negation of Q)

● The changes of state, from one to second, can be made by short impulse to the flip- flop, from outside

● Uses to remember information, where capacity is equal of 1 bit (using 1 flip-flop we can store 1 bit information only))

● not only current values on enter, decide what is the value on exit of flip-

flop, but also the previous state of the flip-flop


The SR flip-flop● The entry placing s (set)

● The entry resetting r (reset)

● The state, when both entries equal 1 is forbidden


The SR flip-flop - 0 and 0 doesn’t change anything


The construction of the flip-flop sr – example of realization with uses of 2 gates (nor)


The construction of the flip-flop sr

remember that 1 and 1 on entry is forbidden


The flip-flop jk

j k Qn Qn+1

0 0 0


The flip-flop jk


Register

● The set of flip-flops, designed to storage, the digital information

● Sequence and Parallel

● Realization of the writing to the parallel register:

- with preliminary resetting

- with the pushed entry


Register

Example of parallel register with preliminary resetting

Before we send data from

one register to next, it is

necessary to reset, the

previous values, stored

in second register.


Register

Example of parallel register with the pushed entry

Resetting is made automatically:

When is 1 we have signal set

When is 0 we have signal reset


Bus connection

● Set of wires, attached in the moment of beginning, of sending the value, to individual exits, of the flip-flops and source

● Applied for making possible of sending the values, between several registers

● The signal is spreads through the wire with the limited speed

● The bus connection is so-called: the long line


The distortion of signals on the Bus connection


Horizontal and impulse signals


Sending the value between Registers

(C) → A wyc, wea from (C) in to A(C) → B wyc, web

wy – horizontal signal we – impulse signal


Coding and decoding – change from one way, of representation the information, to different.

The decoder


Coding and decoding

Using binary values, we can store data in 2 ways:

1. For a set of data, we have the some number of binary values – so it’s one to one.

2. For a set of data, we have combination of binary values.

So having n binary values, we can write n data, using first way, and using second way. Using second, way we can write more different data, but we need to code and decode the information.


The encoder The table of dependence for encoder and decoder


The equation of variables, for encoder and decoder

z0=L1+L3+L5+L7

z1=L2+L3+L6+L7

z2=L4+L5+L6+L7


The realization of encoder and decoder with the use of gates


The summary

● the basis of binary arithmetic

● the logical gates

● the flip-flops

● the registers

● the bus connection

● the encoders and decoders


The Arithmetic-Logic Unit - ALU

● Part of processor that make arithmetic and logic operation on data.

● The basis of binary arithmetic:

In computers is applied the binary system of the representation of integer values, (the mode of replenishment, supplement up 2)

● The basic operation in ALU is the addition

● Subtraction is addition of the opposite number

● The multiplication is the multiple addition of the same number


Basic components of Arithmetic-Logic Unit – ALU

● Two techniques of the realization of the operation on machine words: (n bits n – length of register )

● sequence (old one – bit by bit)

● parallel (operation on n bits in the some time)

● The single module (elementary operator) operates on the single bit of the arguments)

● The register of the accumulator, keeps the results of the operation (sometimes is also one of value)


The versions of the Arithmetic-Logic Unit

● 2-entrance

● With the accumulator as the argument


Arithmetic-Logic Unit

● With the accumulator as the argument


Operations in Arithmetic-Logic Unit - ALU

● The rewriting przep (in) → AK

● The negation not ~(in) → AK

● Logical sum or (Ak) (in) → AK

● Logical product and (Ak) ^ (in) → AK

● The addition dod (Ak) + (in) → AK

● The subtraction ode (Ak)-(in) → AK

weak


The example realization of Arithmetic-Logic Unit – ALU

for the single bit:


The operating memory

Definition of the operating memory:

The technical device, enabling of receiving and recording the data, and then

their inserting, at any moment, to the existing computational process.

Devices that store the programs and data, required by the processors.


The operating memory - Feature of computer memory:

Capacity [Byte – B 1KB =1024B 1MB=1024KB 1GB=1024MB]

Performance

Access time (of writing and reading)

Transfer rate

Physical type

Semiconductor [ROM, RAM, PROM, EPROM, EEPROM]

Magnetic [hard drive disc - HDD]

Optical [DVD]

Physical characteristic

volatile / nonvolatile

erasable / nonerasable

Location [CPU Internal External]


Symbolic of computer operating memory


Sending the value between registers and memory – few examples

(S) → (A) writing to the memory

((A)) → S reading from memory

(S) → 7 writing to the memory to address 7

(3) → S reading from memory from address 3

5 → 2 writing the value 5 to the memory to address 2

(3) → 2 copy data from memory address 3 to the memory to address 2


Sending the value between registers and memory – few examples

• (R1) → R2 sending value from R1 to R2

• ((R1)) →R2 value in R1, is an address of data,

that is in the memory, and we need to send

this data - this value, to R2

• (((R1))) →R2 value in R1, is an address of data1

in the memory, and this data1 is an address of data2

in the memory, and we need to send this data2

- this value, to R2

• R1 → R2 impossible to send R1 to R2 – we can only send the value from R1 (R1)


Semiconductor memory

Volatile:

● RAM (Random Access Memory) – (writing and reading possible)

Nonvolatile:

● ROM (Read Only Memory)

● PROM – (one chance to write data then only reading possible)

● EPROM, EEPROM (writing and reading possible many times)

Theory of Computer Science Basic components of a computer Gate (logical Gate) Flip-flop Register...

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