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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

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Theory of Computer Science - Basic components of a computer Electronic parts (transistors, resistors) -> Gates Gates -> Flip-flop Gates -> Decoder and encoder Gates + Flip-flops -> Register Gates + Flip-flops ->Memory Gates + Flip-flops -> Arithmetic-Logic Unit - ALU Registers + Memory + ALU + Bus connection -> Central Processing Unit - CPU CPU + Memory + Input/Output devices -> computer

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Theory of Computer Science - Basic components of a computer Central Processing Unit - CPU

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer The Gate of negation – NOT The logical function: The change of the entrance signal x on opposite

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Theory of Computer Science - Basic components of a computer 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 xyz

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer The Gate of logical product AND The logical function: z=xy Exit signal y equal 1 only when there are 1 on both entries xyz

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Theory of Computer Science - Basic components of a computer The Gate of logical product AND The logical function: z=xy Exit signal y equal 1 only when there are 1 on both entries

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Theory of Computer Science - Basic components of a computer The Gate of negation of the sum NOR The logical function: Exit signal y equal 1 only when there are 0 on both entries xyz

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Theory of Computer Science - Basic components of a computer The Gate of negation of the sum NOR The logical function: Exit signal y equal 1 only when there are 0 on both entries

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Theory of Computer Science - Basic components of a computer The Gate of negation the products NAND The logical function: Exit signal y equal 0 only when there are 1 on both entries xyz

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Theory of Computer Science - Basic components of a computer The Gate of negation the products NAND The logical function: Exit signal y equal 0 only when there are 1 on both entries

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Theory of Computer Science - Basic components of a computer The Gate of sum modulo 2 XOR The logical function: Exit signal y equal 1 only when there is one on exactly one entry xyz

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Theory of Computer Science - Basic components of a computer The Gate of sum modulo 2 XOR The logical function: Exit signal y equal 1 only when there is one on exactly one entry

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Theory of Computer Science - Basic components of a computer The de Morgan statement: xy

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Theory of Computer Science - Basic components of a computer The de Morgan statement:

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer The SR flip-flop The entry placing s (set) The entry resetting r (reset) The state, when both entries equal 1 is forbidden

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Theory of Computer Science - Basic components of a computer The SR flip-flop - 0 and 0 doesnt change anything

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Theory of Computer Science - Basic components of a computer The construction of the flip-flop sr – example of realization with uses of 2 gates (nor)

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Theory of Computer Science - Basic components of a computer The construction of the flip-flop sr remember that 1 and 1 on entry is forbidden

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Theory of Computer Science - Basic components of a computer The flip-flop jk jkQnQn Q n+1 000

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Theory of Computer Science - Basic components of a computer The flip-flop jk

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer 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.

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer The distortion of signals on the Bus connection

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Theory of Computer Science - Basic components of a computer Horizontal and impulse signals

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Theory of Computer Science - Basic components of a computer Sending the value between Registers (C) A wyc, wea from (C) in to A (C) B wyc, web wy – horizontal signalwe – impulse signal

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Theory of Computer Science - Basic components of a computer Coding and decoding – change from one way, of representation the information, to different. The decoder

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Theory of Computer Science - Basic components of a computer 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 its 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.

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Theory of Computer Science - Basic components of a computer The encoder The table of dependence for encoder and decoder

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Theory of Computer Science - Basic components of a computer The equation of variables, for encoder and decoder z0=L1+L3+L5+L7 z1=L2+L3+L6+L7 z2=L4+L5+L6+L7

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Theory of Computer Science - Basic components of a computer The realization of encoder and decoder with the use of gates

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Theory of Computer Science - Basic components of a computer The summary the basis of binary arithmetic the logical gates the flip-flops the registers the bus connection the encoders and decoders

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer 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)

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Theory of Computer Science - Basic components of a computer The versions of the Arithmetic-Logic Unit 2-entrance With the accumulator as the argument

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Theory of Computer Science - Basic components of a computer Arithmetic-Logic Unit With the accumulator as the argument

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Theory of Computer Science - Basic components of a computer 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

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Theory of Computer Science - Basic components of a computer The example realization of Arithmetic-Logic Unit – ALU for the single bit:

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Theory of Computer Science - Basic components of a computer 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.

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Theory of Computer Science - Basic components of a computer The operating memory - Feature of computer memory: Capacity [Byte – B1KB =1024B1MB=1024KB1GB=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 [CPUInternalExternal]

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Theory of Computer Science - Basic components of a computer Symbolic of computer operating memory

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Theory of Computer Science - Basic components of a computer 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 writing the value 5 to the memory to address 2 (3) 2 copy data from memory address 3 to the memory to address 2

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Theory of Computer Science - Basic components of a computer 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)

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Theory of Computer Science - Basic components of a computer 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)

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