Category: computer Logical Organization

Number System Conversion ”; Previous Next There are many methods or techniques which can be used to convert numbers from one base to another. We”ll demonstrate here the following − Decimal to Other Base System Other Base System to Decimal Other Base System to Non-Decimal Shortcut method − Binary to Octal Shortcut method − Octal to Binary Shortcut method − Binary to Hexadecimal Shortcut method − Hexadecimal to Binary Decimal to Other Base System Steps Step 1 − Divide the decimal number to be converted by the value of the new base. Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number. Step 3 − Divide the quotient of the previous divide by the new base. Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number. Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number. Example − Decimal Number: 2910 Calculating Binary Equivalent − Step Operation Result Remainder Step 1 29 / 2 14 1 Step 2 14 / 2 7 0 Step 3 7 / 2 3 1 Step 4 3 / 2 1 1 Step 5 1 / 2 0 1 As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the Least Significant Digit (LSD) and the last remainder becomes the Most Significant Digit (MSD). Decimal Number − 2910 = Binary Number − 111012. Other Base System to Decimal System Steps Step 1 − Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system). Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns. Step 3 − Sum the products calculated in Step 2. The total is the equivalent value in decimal. Example Binary Number − 111012 Calculating Decimal Equivalent − Step Binary Number Decimal Number Step 1 111012 ((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10 Step 2 111012 (16 + 8 + 4 + 0 + 1)10 Step 3 111012 2910 Binary Number − 111012 = Decimal Number − 2910 Other Base System to Non-Decimal System Steps Step 1 − Convert the original number to a decimal number (base 10). Step 2 − Convert the decimal number so obtained to the new base number. Example Octal Number − 258 Calculating Binary Equivalent − Step 1 − Convert to Decimal Step Octal Number Decimal Number Step 1 258 ((2 × 81) + (5 × 80))10 Step 2 258 (16 + 5 )10 Step 3 258 2110 Octal Number − 258 = Decimal Number − 2110 Step 2 − Convert Decimal to Binary Step Operation Result Remainder Step 1 21 / 2 10 1 Step 2 10 / 2 5 0 Step 3 5 / 2 2 1 Step 4 2 / 2 1 0 Step 5 1 / 2 0 1 Decimal Number − 2110 = Binary Number − 101012 Octal Number − 258 = Binary Number − 101012 Shortcut method – Binary to Octal Steps Step 1 − Divide the binary digits into groups of three (starting from the right). Step 2 − Convert each group of three binary digits to one octal digit. Example Binary Number − 101012 Calculating Octal Equivalent − Step Binary Number Octal Number Step 1 101012 010 101 Step 2 101012 28 58 Step 3 101012 258 Binary Number − 101012 = Octal Number − 258 Shortcut method – Octal to Binary Steps Step 1 − Convert each octal digit to a 3 digit binary number (the octal digits may be treated as decimal for this conversion). Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number. Example Octal Number − 258 Calculating Binary Equivalent − Step Octal Number Binary Number Step 1 258 210 510 Step 2 258 0102 1012 Step 3 258 0101012 Octal Number − 258 = Binary Number − 101012 Shortcut method – Binary to Hexadecimal Steps Step 1 − Divide the binary digits into groups of four (starting from the right). Step 2 − Convert each group of four binary digits to one hexadecimal symbol. Example Binary Number − 101012 Calculating hexadecimal Equivalent − Step Binary Number Hexadecimal Number Step 1 101012 0001 0101 Step 2 101012 110 510 Step 3 101012 1516 Binary Number − 101012 = Hexadecimal Number − 1516 Shortcut method – Hexadecimal to Binary Steps Step 1 − Convert each hexadecimal digit to a 4 digit binary number (the hexadecimal digits may be treated as decimal for this conversion). Step 2 − Combine all the resulting binary groups (of 4 digits each) into a single binary number. Example Hexadecimal Number − 1516 Calculating Binary Equivalent − Step Hexadecimal Number Binary Number Step 1 1516 110 510 Step 2 1516 00012 01012 Step 3 1516 000101012 Hexadecimal Number − 1516 = Binary Number − 101012 Print Page Previous Next Advertisements ”;

Binary Arithmetic ”; Previous Next Binary arithmetic is essential part of all the digital computers and many other digital system. 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 − Addition Binary Subtraction Subtraction and Borrow, these two words will be used very frequently for the binary subtraction. There are four rules of binary subtraction. Example − Subtraction Binary Multiplication Binary multiplication is similar to decimal multiplication. It is simpler than decimal multiplication because only 0s and 1s are involved. There are four rules of binary multiplication. Example − Multiplication Binary Division Binary division is similar to decimal division. It is called as the long division procedure. Example − Division Print Page Previous Next Advertisements ”;

Logic Gates ”; Previous Next Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic. Based on this, logic gates are named as AND gate, OR gate, NOT gate etc. AND Gate A circuit which performs an AND operation is shown in figure. It has n input (n >= 2) and one output. Logic diagram Truth Table OR Gate A circuit which performs an OR operation is shown in figure. It has n input (n >= 2) and one output. Logic diagram Truth Table NOT Gate NOT gate is also known as Inverter. It has one input A and one output Y. Logic diagram Truth Table NAND Gate A NOT-AND operation is known as NAND operation. It has n input (n >= 2) and one output. Logic diagram Truth Table NOR Gate A NOT-OR operation is known as NOR operation. It has n input (n >= 2) and one output. Logic diagram Truth Table XOR Gate XOR or Ex-OR gate is a special type of gate. It can be used in the half adder, full adder and subtractor. The exclusive-OR gate is abbreviated as EX-OR gate or sometime as X-OR gate. It has n input (n >= 2) and one output. Logic diagram Truth Table XNOR Gate XNOR gate is a special type of gate. It can be used in the half adder, full adder and subtractor. The exclusive-NOR gate is abbreviated as EX-NOR gate or sometime as X-NOR gate. It has n input (n >= 2) and one output. Logic diagram Truth Table Print Page Previous Next Advertisements ”;

Hexadecimal Arithmetic ”; Previous Next Hexadecimal Number System Following are the characteristics of a hexadecimal number system. Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. Also called base 16 number system. Each position in a hexadecimal number represents a 0 power of the base (16). Example − 160 Last position in a hexadecimal number represents an x power of the base (16). Example − 16x where x represents the last position – 1. Example Hexadecimal Number − 19FDE16 Calculating Decimal Equivalent − Step Hexadecimal Number Decimal Number Step 1 19FDE16 ((1 × 164) + (9 × 163) + (F × 162) + (D × 161) + (E × 160))10 Step 2 19FDE16 ((1 × 164) + (9 × 163) + (15 × 162) + (13 × 161) + (14 × 160))10 Step 3 19FDE16 (65536 + 36864 + 3840 + 208 + 14)10 Step 4 19FDE16 10646210 Note − 19FDE16 is normally written as 19FDE. Hexadecimal Addition Following hexadecimal addition table will help you greatly to handle Hexadecimal addition. To use this table, simply follow the directions used in this example − Add A16 and 516. Locate A in the X column then locate the 5 in the Y column. The point in ”sum” area where these two columns intersect is the sum of two numbers. A16 + 516 = F16. Example − Addition Hexadecimal Subtraction The subtraction of hexadecimal numbers follow the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 1010. In the binary system, you borrow a group of 210. In the hexadecimal system you borrow a group of 1610. Example – Subtraction Print Page Previous Next Advertisements ”;

Codes Conversion ”; Previous Next There are many methods or techniques which can be used to convert code from one format to another. We”ll demonstrate here the following Binary to BCD Conversion BCD to Binary Conversion BCD to Excess-3 Excess-3 to BCD Binary to BCD Conversion Steps Step 1 — Convert the binary number to decimal. Step 2 — Convert decimal number to BCD. Example − convert (11101)2 to BCD. Step 1 − Convert to Decimal Binary Number − 111012 Calculating Decimal Equivalent − Step Binary Number Decimal Number Step 1 111012 ((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10 Step 2 111012 (16 + 8 + 4 + 0 + 1)10 Step 3 111012 2910 Binary Number − 111012 = Decimal Number − 2910 Step 2 − Convert to BCD Decimal Number − 2910 Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent. Step Decimal Number Conversion Step 1 2910 00102 10012 Step 2 2910 00101001BCD Result (11101)2 = (00101001)BCD BCD to Binary Conversion Steps Step 1 — Convert the BCD number to decimal. Step 2 — Convert decimal to binary. Example − convert (00101001)BCD to Binary. Step 1 – Convert to BCD BCD Number − (00101001)BCD Calculating Decimal Equivalent. Convert each four digit into a group and get decimal equivalent for each group. Step BCD Number Conversion Step 1 (00101001)BCD 00102 10012 Step 2 (00101001)BCD 210 910 Step 3 (00101001)BCD 2910 BCD Number − (00101001)BCD = Decimal Number − 2910 Step 2 – Convert to Binary Used long division method for decimal to binary conversion. Decimal Number − 2910 Calculating Binary Equivalent − Step Operation Result Remainder Step 1 29 / 2 14 1 Step 2 14 / 2 7 0 Step 3 7 / 2 3 1 Step 4 3 / 2 1 1 Step 5 1 / 2 0 1 As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the least significant digit (LSD) and the last remainder becomes the most significant digit (MSD). Decimal Number − 2910 = Binary Number − 111012 Result (00101001)BCD = (11101)2 BCD to Excess-3 Steps Step 1 — Convert BCD to decimal. Step 2 — Add (3)10 to this decimal number. Step 3 — Convert into binary to get excess-3 code. Example − convert (0110)BCD to Excess-3. Step 1 − Convert to decimal (0110)BCD = 610 Step 2 − Add 3 to decimal (6)10 + (3)10 = (9)10 Step 3 − Convert to Excess-3 (9)10 = (1001)2 Result (0110)BCD = (1001)XS-3 Excess-3 to BCD Conversion Steps Step 1 — Subtract (0011)2 from each 4 bit of excess-3 digit to obtain the corresponding BCD code. Example − convert (10011010)XS-3 to BCD. Given XS-3 number = 1 0 0 1 1 0 1 0 Subtract (0011)2 = 1 0 0 1 0 1 1 1 ——————– BCD = 0 1 1 0 0 1 1 1 Result (10011010)XS-3 = (01100111)BCD Print Page Previous Next Advertisements ”;

Memory Devices ”; Previous Next 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 types Internal Memory − cache memory and primary/main memory External Memory − magnetic disk / optical disk etc. Characteristics of Memory Hierarchy are following when we go from top to bottom. Capacity in terms of storage increases. Cost per bit of storage decreases. Frequency of access of the memory by the CPU decreases. Access time by the CPU increases. 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) 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. Inside the PROM chip there are small fuses which are burnt open during programming. It can be programmed only once and is not erasable. 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. Serial Access Memory Sequential access means the system must search the storage device from the beginning of the memory address until it finds the required piece of data. Memory device which supports such access is called a Sequential Access Memory or Serial Access Memory. Magnetic tape is an example of serial access memory. Direct Access Memory Direct access memory or Random Access Memory, refers to conditions in which a system can go directly to the information that the user wants. Memory device which supports such access is called a Direct Access Memory. Magnetic disks, optical disks are examples of direct access memory. 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.

Digital Number System ”; Previous Next A digital system can understand positional number system only where there are a few symbols called digits and these symbols represent different values depending on the position they occupy in the number. A value of each digit in a number can be determined using The digit The position of the digit in the number The base of the number system (where base is defined as the total number of digits available in the number system). Decimal Number System The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represents units, tens, hundreds, thousands and so on. Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position, and its value can be written as (1&times1000) + (2&times100) + (3&times10) + (4&timesl) (1&times103) + (2&times102) + (3&times101) + (4&timesl00) 1000 + 200 + 30 + 1 1234 As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers. S.N. Number System & Description 1 Binary Number System Base 2. Digits used: 0, 1 2 Octal Number System Base 8. Digits used: 0 to 7 3 Hexa Decimal Number System Base 16. Digits used: 0 to 9, Letters used: A- F Binary Number System Characteristics Uses two digits, 0 and 1. Also called base 2 number system Each position in a binary number represents a 0 power of the base (2). Example: 20 Last position in a binary number represents an x power of the base (2). Example: 2x where x represents the last position – 1. Example Binary Number: 101012 Calculating Decimal Equivalent − Step Binary Number Decimal Number Step 1 101012 ((1 &times 24) + (0 &times 23) + (1 &times 22) + (0 &times 21) + (1 &times 20))10 Step 2 101012 (16 + 0 + 4 + 0 + 1)10 Step 3 101012 2110 Note: 101012 is normally written as 10101. Octal Number System Characteristics Uses eight digits, 0,1,2,3,4,5,6,7. Also called base 8 number system Each position in an octal number represents a 0 power of the base (8). Example: 80 Last position in an octal number represents an x power of the base (8). Example: 8x where x represents the last position – 1. Example Octal Number − 125708 Calculating Decimal Equivalent − Step Octal Number Decimal Number Step 1 125708 ((1 × 84) + (2 × 83) + (5 × 82) + (7 × 81) + (0 × 80))10 Step 2 125708 (4096 + 1024 + 320 + 56 + 0)10 Step 3 125708 549610 Note: 125708 is normally written as 12570. Hexadecimal Number System Characteristics Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. Also called base 16 number system. Each position in a hexadecimal number represents a 0 power of the base (16). Example 160. Last position in a hexadecimal number represents an x power of the base (16). Example 16x where x represents the last position – 1. Example − Hexadecimal Number: 19FDE16 Calculating Decimal Equivalent − Step Hexadecimal Number Decimal Number Step 1 19FDE16 ((1 × 164) + (9 × 163) + (F × 162) + (D × 161) + (E × 160))10 Step 2 19FDE16 ((1 × 164) + (9 × 163) + (15 × 162) + (13 × 161) + (14 × 160))10 Step 3 19FDE16 (65536 + 36864 + 3840 + 208 + 14)10 Step 4 19FDE16 10646210 Note − 19FDE16 is normally written as 19FDE. Print Page Previous Next Advertisements ”;

Computer Logical Organization Tutorial PDF Version Quick Guide Resources Job Search Discussion Computer Logical Organization refers to the level of abstraction above the digital logic level, but below the operating system level. At this level, the major components are functional units or subsystems that correspond to specific pieces of hardware built from the lower level building blocks. This tutorial gives a complete understanding on Computer Logical Organization starting from basic computer overview till its advanced architecture. Audience This reference has been prepared for the students pursing either Bachelors or Masters in Computer Science to help them understand the basic-to-advanced concepts related to Computer Logical Organization. Prerequisites Before you start proceeding with this tutorial, I”m making an assumption that you are already aware of basic computer concepts like what is keyboard, mouse, monitor, input, output, primary memory, secondary memory, etc. If you are not well aware of these concepts, then I will suggest you to go through our short tutorial on Computer Fundamentals. Print Page Previous Next Advertisements ”;

Binary Codes ”; Previous Next 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 Following is the list of advantages that binary code offers. 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. Classification of binary codes The codes are broadly categorized into following four categories. Weighted Codes Non-Weighted Codes Binary Coded Decimal Code Alphanumeric Codes Error Detecting Codes Error Correcting Codes Weighted Codes Weighted binary codes are those binary codes which obey the positional weight principle. Each position of the number represents a specific weight. Several systems of the codes are used to express the decimal digits 0 through 9. In these codes each decimal digit is represented by a group of four bits. Non-Weighted Codes In this type of binary codes, the positional weights are not assigned. The examples of non-weighted codes are Excess-3 code and Gray code. Excess-3 code The Excess-3 code is also called as XS-3 code. It is non-weighted code used to express decimal numbers. The Excess-3 code words are derived from the 8421 BCD code words adding (0011)2 or (3)10 to each code word in 8421. The excess-3 codes are obtained as follows − Example Gray Code It is the non-weighted code and it is not arithmetic codes. That means there are no specific weights assigned to the bit position. It has a very special feature that, only one bit will change each time the decimal number is incremented as shown in fig. As only one bit changes at a time, the gray code is called as a unit distance code. The gray code is a cyclic code. Gray code cannot be used for arithmetic operation. Application of Gray code Gray code is popularly used in the shaft position encoders. A shaft position encoder produces a code word which represents the angular position of the shaft. Binary 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 Codes It is very similar to decimal system. We need to remember binary equivalent of decimal numbers 0 to 9 only. Disadvantages of BCD Codes The addition and subtraction of BCD have different rules. The BCD arithmetic is little more complicated. BCD needs more number of bits than binary to represent the decimal number. So BCD is less efficient than binary. Alphanumeric codes A binary digit or bit can represent only two symbols as it has only two states ”0” or ”1”. But this is not enough for communication between two computers because there we need many more symbols for communication. These symbols are required to represent 26 alphabets with capital and small letters, numbers from 0 to 9, punctuation marks and other symbols. The alphanumeric codes are the codes that represent numbers and alphabetic characters. Mostly such codes also represent other characters such as symbol and various instructions necessary for conveying information. An alphanumeric code should at least represent 10 digits and 26 letters of alphabet i.e. total 36 items. The following three alphanumeric codes are very commonly used for the data representation. American Standard Code for Information Interchange (ASCII). Extended Binary Coded Decimal Interchange Code (EBCDIC). Five bit Baudot Code. 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. Error Codes There are binary code techniques available to detect and correct data during data transmission. Error Code Description Error Detection and Correction Error detection and correction code techniques Print Page Previous Next Advertisements ”;