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Octal Number System:

It is a system with base 8. This number system has 8 digits from (0-7). It is a shorthand method of expressing binary quantities.

In this system, there exist 8 combinations of 3-bit binary numbers. 
The octal number (20)₈ can be converted to a decimal number as follows:

(20)₈ = 2 * 8¹ +0 * 8⁰

            =  16+0

            = (16)₁₀

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The differences between the Binary Number System and Decimal Number System are as follows:

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The amount of time that it takes for the memory to produce the data required, from the start of the access until when the valid data is available for use, is called the memory's access time, sometimes abbreviated as ta.

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A dot matrix printer is a most popular serial printer i.e., it prints one character at a time.

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Magnetic tape has been used for data storage for over 50 years.

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It is a form of computer that uses continuous physical phenomena such as electrical and mechanical quantities to model the problem being solved.

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In impact printer, there is a mechanical contact between the print head and the paper.

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MICR stands for Magnetic Ink Character Reader. It is a character reading technology adopted mainly by the banking industry to facilitate the processing of cheques.

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Parallel ports can send or receive a byte (8 bit) at a time. Unlike, the serial port these 8 bits are transmitted parallel to each other.

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A serial port is a serial communication physical interface through which information transfers in or out one bit at a time.

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A parallel port is a type of interface found on computers for connecting various peripherals.

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Parallel ports can send or receive a byte (8 bits) at a time. Unlike the serial port, these 8 bits are transmitted parallel to each other.

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1x(2^0) +1x(2^1)+0x (2^2) + 1x (2^3) + 0x(2^4) + 1x(2^5)=43.

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Divide successively by 2 and write the remainders from bottom to up.

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Multiple each digit with the weights of 2.

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Group the number into fours. Write the corresponding hexadecimal equivalent.

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Group the number into fours. Write the corresponding hexadecimal equivalent. Here binary number 1010 = A and 1011 = B

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Divide successively by 2 and write the remainders from bottom to top.

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Divide successively by 2 and write the remainders from bottom to top.

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Group the number into fours. Write the corresponding hexadecimal equivalent.

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Group the number into fours. Write the corresponding hexadecimal equivalent. 1011 1010 1111 is equivalent to B A F.

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Divide successively by 2 and write the remainders from top to down.

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Divide successively by 2 and write the remainders from top to down.

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First of all, grouping of numbers in four digits group is done, i.e., 11,0111,1010,1110. The number is converted to 37AE. Thus, the solution is 37AE.

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The positive expression of number is 00010001. Its complement is 11101110.

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Group the number into fours. Write the corresponding hexadecimal equivalent.

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The hexadecimal system is also a positional value system, wherein each hexadecimal digit has its own value or weight expressed as a power of 16.

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Bit is a binary digit, taking a logical value of either "1" or "0" (also referred to as "true" or "false" respectively). Binary digits are a basic unit of information storage and communication in digital computing and digital information theory.

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The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0,1,2,3,4,5,6,8,9; using these symbols as digits of a number, we can express any quantity.

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The rightmost digit of a decimal number is known as the Most Significant Digit.

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The leftmost digit in a decimal number is referred to as the Least Significant Digit.

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In 25.12, the decimal point is used to separate 25 and 12, i.e., integer and fractional part of the number.

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Group into 4 and express the groups in hexadecimal. 1010 = A, 1011 = B and 01 = 2

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Divide into groups of three starting from left to right and express the groups in decimal. 1011110100011 can be grouped as 1 011 110 100 011, i.e., 13643

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0x(2^0) +1x(2^1)+0x (2^2) + 1x (2^3) + 0x(2^4) + 1x(2^5)=42.

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Divide successively by 2 and write the remainders from top to down.

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Divide successively by 2 and write the remainders from top to down.

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Convert 225 to binary and then .35 to its binary equivalent. Divide 225 by 2 and multiply .35 by 2 and collect all numbers to the left of the decimal point, reading down.

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Decimal numbers are represented in ASCII starting from 011.

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In n bits format, one can store 2^n-1 bits.

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To obtain the 2’s complement of a number, first reverse the bits and then add 1 to it.

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ASCII code is a 7-bit code. It codes 2^7 bits ranging from 0 to 127.

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Java code is written in Unicode to make it a portable language.

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FF is a hexadecimal representation.

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ASCII code is a 7-bit code.

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In hexadecimal number system, F represents 15.

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A byte is a unit of information storage in computers. 8 bits make 1 byte.

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It uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three.

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The machine language converts the numbers in binary format as computer understands only binary form, i.e., 0 and 1.

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An octal number system has 2^3=8 digits.

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Group into four and write their hex equivalent. 11011110101110 can be divided as 11 0111 1010 1110 which is equal to 3 7 A E .

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The machine first converts 22 into binary, then .25 into binary equivalent.

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This is the conventional form for number representation. Integers are identified by their signs (+ or -) & a string of digits, which represent the magnitude.
For example:
+18 or 46 are Positive Integers.
-16 or –78 are Negative Integers

For example: +15 will be represented in following way.

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Each hex digit is converted to its 4-digit binary equivalent.
For example:
          (9F2)₁₆ =   9           F        2 

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 1. First convert the decimal number to its binary equivalent by repeated division method.

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 Groups in forms            10, 1011, 1010
       Convert each number     2,      B,      A
       Thus, the solution is 2 BA.

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Binary numbers can be converted to hexadecimal numbers by grouping in groups of four each starting from the right and then writing the equivalent hexadecimal digit to every group of four bits.

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 It will be converted as follows:
       (56.08) ₁₆   = 5 x (16) ¹ + 6 x (16) ⁰ + 0 x (16)^-1 + 8 x (16)^-2

                       = 80 + 6 + 0 + 8/256

                       = 86 + 0.03125

                       = (86.03125) ₁₀

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A hex digit position has a weight that is a power of 16. The LSD has a weight of 16⁰ = 1, the next higher digit has a weight of 16¹ = 16, the next higher digit has a weight of 16² = 256, and so on. For example:
          (356) ₁₆ = 3 x (16) ² + 5 x (16) ¹ + 6 x (16) ⁰

                      = 768 + 80 + 6

                      = (854) ₁₀

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Decimal to hexadecimal can be done by using repeated division by 16.

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The procedure followed to convert a binary to its octal equivalent is simply reverse of what we follow for binary to octal conversions. The bits of the binary integer are grouped into groups of three bits each starting at the LSB. Then, each group is converted to its octal equivalent.

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The conversion from octal to binary is performed by converting each octal digit to its 3-digit binary equivalent. The eight possible digits are converted as in the table below :

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 An octal number can be converted to its decimal equivalent by multiplying each octal by its positional weight.
          (372) ₈ = 3 x (8)² + 7x (8)¹ + 2 x (8)⁰

                    = 3 x 64 + 7 x 8 + 2 x 1

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 Original number is 0.375,                                           Integer Part
       Multiply (fractional part) 0.015625 by 8     = 0.125              0
       Multiply (fractional part) 0.125 by 8 = 1.0                          0

       Reading down,
        (0.015625) ₁₀ = (0.01) ₈

SOLUTION

 = 1 x (2) ³ + 1 x (2) ² + 0 x (2) ¹ + 1 x (2) ⁰ + 0 x (2)^-1 + 0 x (2)^-2 + 0 x (2)^-3 + 1 x (2)^-4  + 0 x (2)^-5 + 1 x (2)^-6
       = 8 + 4 + 0 + 1 + 0 + 0 + 0 + 1/16 + 0 + 1/64

       = 13 + 0.0625 + 0.015625

       = (13.078125) ₁₀
        (1101.000101) ₂ = (13.078125) ₁₀

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In this method, the number is divided again & again by 2, & its remainders are recorded, until the remainder becomes zero. The final binary result is obtained by assembling all the remainders, with the last remainder, with the last remainder being the most significant bit (MSB).

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 (11011) ₂    (binary)
       (2) ⁴ + (2) ³ + (2) ² + (2) ¹ + (2) ⁰    = 16+8+2+1 

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The hexadecimal number (2B)₁₆  can be converted to decimal number as follows:

  (2B)₁₆ = 2 * 16¹ +11 * 16⁰

            =  32+11

            = (43)₁₀

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The octal number 24 can be converted to decimal as follows:

(24)₈ = (2 * 8¹ + 4 * 8⁰) 

       =(16 + 4)
       =(20)₁₀

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The binary number 1001 can be converted to decimal as follows:

(1001)₂  = (1 * 2³ + 0 * 2²+ 0 * 2¹ + 1 * 2⁰) 

             = (8 +0+0+1)

             =(9)

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Serial ports transfer data serially a bit at a time. Serial ports provide a standard connector and protocol to let you attach devices, such as modems, to your computer.

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It is a serial communication physical interface through which information transfers in or out one bit at a time.

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A port serves as an interface between the computer and other computers or peripheral devices.

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Digital Video Disk or DVD is an optical disc storage media format. DVD's were originally developed for the movie industry. Huge capacity makes them attractive for storing large amounts of data.

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The number of bits a memory word consists of is known as word length. Memory addresses are consecutive numbers, starting with the address 0, 1, 2, ... and running upto the largest addresses. Thus, at address 0, we find the first word; at address 1, the second word; at address 2, the third word; at address 3 and so on.

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A port is an application-specific or a process-specific software construct to serve as a communications endpoint used by transport layer protocols of the Internet Protocol Suite such as Transmission Control Protocol (TCP) and User Datagram Protocol (UDP).

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A scanner scans an image and we can save it on a computer.

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CDROM is used to store information and cannot be used to modify it.

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A data storage device is used to store data and its related information.

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A DRAM needs to be refreshed because the capacitors lose their charge over time.

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Word Length is the number of bits in a word. It stores the information in the word. The amount of information is the word length.

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A bit is a binary digit, taking a value of either 0 or 1. Binary digits are a basic unit of information storage and communication in digital computing.

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Electrostatic printers are instruments, which are used to print an optical image on a specially treated paper. Electro-statically charged and uncharged portions of the paper illustrate light and dark portions of the original image.

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It is a storage device used by a computer to hold the currently executing program and its working data.

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It is a short form for Extended Data Out Dynamic Random Access Memory. Conventional DRAM cells discharge after each read operation and requires refreshing time before it can be read again.

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A floppy disk is a data storage medium that is composed of a disk of thin, flexible ("floppy") magnetic storage medium encased in a square or rectangular plastic shell. It can store upto 1.44 MB of data.

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CD-RW is erasable disk. It can also be called as the rewritable media.

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Bluetooth provides an agreement at the protocol level, where products have to agree on when bits are sent, how many will be sent at a time and how the parties in conversation can be sure, that the message received is the same as the message sent.

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A PS/2 (Personal System/2) port is an electronic receptacle or plug found on computers. It accepts a PS/2 with a mini-DIN connector and is most often used to plug in a keyboard or mouse.

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IR Ports are special type of ports in which a focused ray of light is modulated with information.

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A method of representing numbers in which only the digits 0 and 1 are used. Successive units are powers of 2.

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Binary Number System

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Number system is a system of representing numbers, for example the decimal system or the binary system.

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In a computer, data is represented by different number system.Like Binary number system, Octal number system and so on.

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Data are raw facts and figures used for processing to get information.

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We can represent an integer in the following ways :
       a. Sign & magnitude representation
       b. One’1 complement representation      
       c. Two’s compliment representation

SOLUTION

 1 x (2) ³ + 0 x (2) ² + 1 x (2) ¹ + 0 x (2) ⁰ + 0 x (2)^-1 + 1 x (2)^-2 + 0 x (2)^-3 + 1 x (2)^-4 
       = 8+0+2+0+0+0.25+0+0.625
       = 10.3125₁₀