unit v computer, number system

COMPUTER, NUMBER SYSTEM

UNIT- V

Fundamental of Computer programming -206

By- Er. Indrajeet Sinha , +919509010997

CONTENT:- Computer, Stored Program Architecture Storage Devices – primary memory and secondary stora

concept of radix and representation of numbers System Conversion from radix r1 to radix r2 Binary Arithmetic Complements Representation of Alphabets

INTRODUCTION TO COMPUTER, STORED PROGRAM ARCHITECTURE

Lecture no.- 39, UNIT- V

5.1.1- What is a computer? Definition:-

Computer is an electronic device that is designed to work with Information. The term computer is derived from the Latin term‘ computare’, this means to calculate or programmable machine.

For more click Here 4

5.1.2- Stored Program Architecture Stored program concept:

Stored-program concept is designed by Hungarian mathematician John Von Neumann.

The von Neumann architecture is a design model for a stored-program digital computer that uses a processing unit and a single separate storage structure to hold both instructions and data.

A stored-program digital computer is one that keeps its programmed instructions, as well as its data, in read-write, random access memory (RAM).

6von Neumann architecture

STORAGE DEVICES – PRIMARY MEMORY AND SECONDARY STORAGE

Definition: A memory is just like a human brain. It is used to store

data and instruction. Computer memory is the storage space in computer where data is to be processed and instructions required for processing are stored.

The memory is divided into large number of small parts. Each part is called a cell. Each location or cell has a unique address which varies from zero to memory size minus one.

For example if computer has 64k words, then this memory unit has 64 * 1024 = 65536 memory location. The address of these locations varies from 0 to 65535.

Memory is primarily of two typesInternal Memory − cache memory and primary/main

memoryExternal Memory − magnetic disk / optical disk etc.

Characteristics of Memory Hierarchy are following when we go from top to bottom..

1. Capacity in terms of storage increases.2. Cost per bit of storage decreases.3. Frequency of access of the memory by the CPU

decreases.4. Access time by the CPU increases.

5.2.1 TYPES OF MEMORY

RAM A RAM constitutes the internal memory of the CPU for storing

data, program and program result. It is read/write memory. It is called random access memory (RAM).

Since access time in RAM is independent of the address to the word that is, each storage location inside the memory is as easy to reach as other location & takes the same amount of time. We can reach into the memory at random & extremely fast but can also be quite expensive.

RAM is volatile, i.e. data stored in it is lost when we switch off the computer or if there is a power failure. Hence, a backup uninterruptible power system (UPS) is often used with computers. RAM is small, both in terms of its physical size and in the amount of data it can hold.

RAM is of two types Static RAM (SRAM) Dynamic RAM (DRAM) 12

Static RAM (SRAM) The word static indicates that the memory retains its contents as

long as power remains applied. However, data is lost when the power gets down due to volatile nature. SRAM chips use a matrix of 6-transistors and no capacitors. Transistors do not require power to prevent leakage, so SRAM need not have to be refreshed on a regular basis.

Because of the extra space in the matrix, SRAM uses more chips than DRAM for the same amount of storage space, thus making the manufacturing costs higher.

Static RAM is used as cache memory needs to be very fast and small.

Dynamic RAM (DRAM) DRAM, unlike SRAM, must be continually refreshed in order for it

to maintain the data. This is done by placing the memory on a refresh circuit that rewrites the data several hundred times per second. DRAM is used for most system memory because it is cheap and small. All DRAMs are made up of memory cells. These cells are composed of one capacitor and one transistor.

ROM ROM stands for Read Only Memory. The memory from which we

can only read but cannot write on it. This type of memory is non-volatile. The information is stored permanently in such memories during manufacture.

A ROM, stores such instruction as are required to start computer when electricity is first turned on, this operation is referred to as bootstrap. ROM chip are not only used in the computer but also in other electronic items like washing machine and microwave oven.

Following are the various types of ROM − MROM (Masked ROM) The very first ROMs were hard-wired devices that contained a pre-

programmed set of data or instructions. These kind of ROMs are known as masked ROMs. It is inexpensive ROM.

PROM (Programmable Read Only Memory) PROM is read-only memory that can be modified only once by a

user. The user buys a blank PROM and enters the desired contents using a PROM programmer.

EPROM (Erasable and Programmable Read Only Memory)

The EPROM can be erased by exposing it to ultra-violet light for a duration of upto 40 minutes. Usually, an EPROM eraser achieves this function. During programming an electrical charge is trapped in an insulated gate region. The charge is retained for more than ten years because the charge has no leakage path. For erasing this charge, ultra-violet light is passed through a quartz crystal window (lid). This exposure to ultra-violet light dissipates the charge. During normal use the quartz lid is sealed with a sticker.

EEPROM (Electrically Erasable and Programmable Read Only Memory)

The EEPROM is programmed and erased electrically. It can be erased and reprogrammed about ten thousand times. Both erasing and programming take about 4 to 10 ms (millisecond). In EEPROM, any location can be selectively erased and programmed. EEPROMs can be erased one byte at a time, rather than erasing the entire chip. Hence, the process of re-programming is flexible but slow.

Cache Memory Cache memory is a very high speed semiconductor

memory which can speed up CPU. It acts as a buffer between the CPU and main memory. It is used to hold those parts of data and program which are most frequently used by CPU. The parts of data and programs, are transferred from disk to cache memory by operating system, from where CPU can access them.

Advantages Cache memory is faster than main memory. It consumes less access time as compared to main

memory. It stores the program that can be executed within a short

period of time. It stores data for temporary use.

Disadvantages Cache memory has limited capacity. It is very expensive.

Virtual memory is a technique that allows the execution of processes which are not completely available in memory. The main visible advantage of this scheme is that programs can be larger than physical memory. Virtual memory is the separation of user logical memory from physical memory.

Auxiliary Memory Auxiliary memory is much larger in size than main memory but is

slower. It normally stores system programs, instruction and data files. It is also known as secondary memory. It can also be used as an overflow/virtual memory in case the main memory capacity has been exceeded.

Characteristics of Auxiliary Memory are following − Non-volatile memory − Data is not lost when power is cut off. Reusable − The data stays in the secondary storage on

permanent basis until it is not overwritten or deleted by the user. Reliable − Data in secondary storage is safe because of high

physical stability of secondary storage device. Convenience − With the help of a computer software,

authorised people can locate and access the data quickly. Capacity − Secondary storage can store large volumes of data

in sets of multiple disks. Cost − It is much lesser expensive to store data on a tape or

disk than primary memory. 19

NUMBER SYSTEM

5.5.1- NON POSITIONAL AND POSITIONAL NUMBER SYSTEM

Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.

Definition: A positional number system gives different meaning

to the same symbol depending on its position. A 1 in the right most or zero position means one, a 1 in the 3rd position from the right (100) means one hundred.

An example of non positional number system is the number system of Romans. Here different letters have always the same value. For instance 3 is III, so the letter I has always the same value, 1.For instance 4 is IV, where V means 5 but the other number I before subtracts 1 to it, yielding 4. 21

5.5.3 DECIMAL NUMBER SYSTEMDefinition

Decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

A Binary number system has only two digits that are 0 and 1. Every number (value) represents with 0 and 1 in this number system. The base of binary number system is 2, because it has only two digits.

Octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has only 8 digits.

CONTT.. A Hexadecimal number system has sixteen (16)

alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of hexadecimal number system is 16, because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 14, E is 15 and F is 16.

SUMMARY….

Number system Base Used digits Example C Language

assignment

Binary 2 0,1 (11110000)2

int val=0b11110000;

Octal 8 0,1,2,3,4,5,6,7 (360)8 int val=0360;

Decimal 10 0,1,2,3,4,5,6,7,8,9 (240)10 int val=240;

Hexadecimal 16

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

(F0)16 int val=0xF0;

CONVERSION FROM RADIX R1 TO RADIX R2

5.6.1 CONVERSION FROM ONE NUMBER SYSTEM TO ANOTHER

Decimal Number System to Other Base

To convert Number system from Decimal Number System to Any Other Base is quite easy; you have to follow just two steps:

A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).

B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last as a Most Significant Bit (MSB).

Decimal to Binary ConversionDecimal Number is : (12345)10

Binary Number is(11000000111001)2

Decimal to Octal Conversion Decimal Number is : (12345)10

Octal Number is(30071)8

Decimal to Hexadecimal Conversion Decimal Number is : (12345)10

Hexadecimal Number is(3039)16

Hexadecimal Number is(2D5)16 Convert10, 11, 12, 13, 14, 15to its equivalent...A, B, C, D, E, F

Other Base System to Decimal Number Base To convert Number System from Any Other Base System to Decimal

Number System, you have to follow just three steps:

A) Determine the base value of source Number System (that you want to convert), and also determine the position of digits from LSB (first digit’s position – 0, second digit’s position – 1 and so on).

B) Multiply each digit with its corresponding multiplication of position value and Base of Source Number System’s Base.

C) Add the resulted value in step-B.

Explanation regarding examples:Below given exams contains the following rows:A) Row 1 contains the DIGITs of number (that is going to be converted). B) Row 2 contains the POSITION of each digit in the number system.C) Row 3 contains the multiplication: DIGIT* BASE^POSITION.D) Row 4 contains the calculated result of step C.E) And then add each value of step D, resulted value is the Decimal Number.

Binary to Decimal Conversion Binary Number is : (11000000111001)2

Octal to Decimal Conversion Octal Number is : (30071)8

=12288+0+0+56+1=12345Decimal Number is: (12345)10

Hexadecimal to Decimal Conversion Hexadecimal Number is : (2D5)16

=512+208+5=725Decimal Number is: (725)10

BINARY ARITHMETIC

5.7.1- BINARY ADDITION

It is a key for binary subtraction, multiplication, division. There are four rules of binary addition.

In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next column.

Example

Binary Subtraction

Example:-

Binary Multiplication

Example:

Binary Division

Octal ArithmeticHexaArithmetic

R’S AND (R-1)’S COMPLEMENT

5.8.1 COMPLEMENTS Complements are used in the digital computers in order

to simplify the subtraction operation and for the logical manipulations. For each radix-r system (radix r represents base of number system) there are two types of complements.

S.N. Complement Description1 Radix

ComplementThe radix complement is referred to as the r's complement

2 Diminished Radix Complement

The diminished radix complement is referred to as the (r-1)'s complement

2 REPRESENTATION OF INTEGERS (SIGNED AND UNSIGNED)

Sign-Magnitude Representation There are many schemes for representing negative

integers with patterns of bits. One scheme is sign-magnitude. It uses one bit (usually the leftmost) to indicate the sign. "0" indicates a positive integer, and "1" indicates a negative integer.

The rest of the bits are used for the magnitude of the number.

So -2410 is represented as: 1001 1000 The sign "1" means negative The magnitude

is 24 (in 7-bit binary)

5.8.2.2 SIGNED-1’S COMPLEMENT Binary system complements:

As the binary system has base r = 2. So the two types of complements for the binary system are 2's complement and 1's complement.

1's complement The 1's complement of a number is found by changing all

1's to 0's and all 0's to 1's. This is called as taking complement or 1's complement. Example of 1's Complement is as follows.

5.8.2.3- SIGNED-2’S COMPLEMENT2's complement The 2's complement of binary number is obtained by

adding 1 to the Least Significant Bit (LSB) of 1's complement of the number.

2's complement = 1's complement + 1

REPRESENTATION OF ALPHABETS

5.9 - INTRODUCTION In the coding, when numbers, letters or words are

represented by a specific group of symbols, it is said that the number, letter or word is being encoded.

The group of symbols is called as a code. The digital data is represented, stored and transmitted as group of binary bits. This group is also called as binary code.

The binary code is represented by the number as well as alphanumeric letter.

Advantages of Binary Code

Binary codes are suitable for the computer applications. Binary codes are suitable for the digital communications. Binary codes make the analysis and designing of digital

circuits if we use the binary codes. Since only 0 & 1 are being used, implementation

becomes easy. 46

5.9.1- BCD CODEBinary Coded Decimal (BCD) code In this code each decimal digit is represented by a 4-bit

binary number. BCD is a way to express each of the decimal digits with a binary code. In the BCD, with four bits we can represent sixteen numbers (0000 to 1111). But in BCD code only first ten of these are used (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in BCD.

Advantages of BCD Codes1. It is very similar to decimal system.2. We need to remember binary equivalent of decimal numbers 0 to 9

only.47

Disadvantages of BCD Codes1. The addition and subtraction of BCD have different

rules.2. The BCD arithmetic is little more complicated.3. BCD needs more number of bits than binary to

represent the decimal number. So BCD is less efficient than binary.

5.9.2 ASCII CODE ASCII stands for American Standard Code for

Information Interchange. There are 128 standard ASCII codes, each of which can be represented by a 7 digit binary number: 0000000 through 1111111.

Extended ASCII adds an additional 128 characters that vary between computers, programs and fonts.

To See ASCII Table Click Here

5.9.3 EBCDIC CODE Definition: The extended binary coded decimal interchange code

(EBCDIC) is an 8-bit alphanumeric code which has been extensively used by IBM in its mainframe applications.

ASCII code is a 7-bit code whereas EBCDIC is an 8-bit code. ASCII code is more commonly used worldwide while EBCDIC is used primarily in large IBM computers.

Char EBCDIC HEX Char EBC

DIC HEX Char EBCDIC HEX

A 1100 0001 C1 P 1101

0111 D7 4 1111 0100 F4

B 1100 0010 C2 Q 1101

1000 D8 5 1111 0101 F5

C 1100 0011 C3 R 1101

1001 D9 6 1111 0110 F6

D 1100 0100 C4 S 1110

0010 E2 7 1111 0111 F7

E 1100 0101 C5 T 1110

0011 E3 8 1111 1000 F8

F 1100 0110 C6 U 1110

0100 E4 9 1111 1001 F9

G 1100 0111 C7 V 1110

0101 E5 blank ... ...

H 1100 1000 C8 W 1110

0110 E6 . ... ...

I 1100 1001 C9 X 1110

0111 E7 ( ... ...52

Char EBCDIC HEX Char EBCDIC HEX Char EBC

DIC HEX

J 1101 0001 D1 Y 1110

1000 E8 + ... ...

K 1101 0010 D2 Z 1110

1001 E9 $ ... ...

L 1101 0011 D3 0 1111

0000 F0 * ... ...

M 1101 0100 D4 1 1111

0001 F1 ) ... ...

N 1101 0101 D5 2 1111

0010 F2 - ... ...

O 1101 0110 D6 3 1111

0011 F3 / ... ...

CONCLUSION OF UNIT-5

We study different type of number system. Arithmetic operation on no. system.

unit v computer, number system

Engineering

unit-ii computer architecture and organization … ·...

computer networks unit-1

unit 3 computer applications

henry brady computer components unit 2 – computer systems

unit 1 computer users

computer number systems

unit - i digital computer...

unit 3 computer systems

ch09 computer arithmetic cpu combines of alu and control...

unit -3 computer software

unit 3 computer systems

u.s. naval acade.my computer science department technical...

unit i computer programming: computer programs are written

computer components unit 1: human computer interactions

unit 1: computer basics

unit- i introduction to computer graphics unit i ...1...

unit 2 computer software

unit (3) computer-assisted language learning...

computer controlled saturation pressure unit, with … ·...

unit 2: computer hardware...