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+1 Computer Application, Chapter 1, , Fundamentals of Computer, With Short Note
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Number System, A number is a mathematical object used to count,, label and measure., A number system is a systematic way to represent, numbers.
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The number system we use in our day to day, life is the decimal number system., Symbols/, Digit, , The number of symbols used in a number system is, called base or radix of a number system.
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Number Systems
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Decimal Number System, , Place value of each decimal digit is power of 10 (10 0 , 10 1 , 10 2 , ...).
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Consider a number 5876, , The digit with most weight is called Most Significant Digit(MSD), and the digit with least weight is called Least Significant Digit (LSD)., , In 5876 ,5 is the MSD and 6 is LSD
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10-1=0.1, 10-2=0.01, 10-3=0.001, Left most digit of a number is MSD and right most digit of a number is LSD
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Binary Number System, , Each digit in binary number system is called a bit., Bit stands for binary digit, Computer uses binary number system as the basic number system, for data representation.
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Consider a binary number (1101)2 . It can be written in expandable, form as shown below, , The left most bit is MSB, The right most bit is LSB
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2-1=0.5, 2-2=0.25, 2-3=0.125
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Octal Number System
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0.125, , 8-1=0.125
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0.0625, , 16-1=0.0625, , The weight of a digit depends on its relative position., Such a number system is known as positional number system.
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Decimal to Binary Conversion, , Convert 25 to binary
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In this method the decimal number is repeatedly divided by 2 and the, remainders are recorded.
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Convert 80 to binary
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34= (100010)2, , 125= (1111101)2, , Binary equivalent of an odd decimal number ends with 1 and binary, of even decimal number ends with zero., Qn 1. Convert 127 to binary
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Decimal to Octal Conversion, Convert 125 to octal
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Convert 400 to octal, , In this method the decimal number is repeatedly divided by 8 and the, remainders are recorded., Qn 2. Convert 259 to octal
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Convert 380 to Hexa Decimal, , In this method the decimal number is repeatedly divided by 16 and the, remainders are recorded., Qn 3. Convert 174 to hexa decimal
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Binary to Decimal Conversion
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A binary number can be converted into its decimal, equivalent by summing up the product of each bit and, its weight.
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Qn 4. Convert (101011)2 to decimal
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Octal to Decimal Conversion, , An octal number can be converted into its decimal equivalent by summing up the, product of each octal digit and its weight
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Hexa Decimal to Decimal Conversion, , An hexadecimal number can be converted into its decimal equivalent by summing up, the product of each hexadecimal digit and its weight.
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Octal to Binary Conversion, , An octal number can be converted into binary by converting each octal, digit to its 3 bit binary equivalent.
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Qn 7. Convert (371)8 to binary
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Hexa Decimal to Binary Conversion, , An hexa decimal number can be converted into binary by converting each, hexa decimal digit to its 4 bit binary equivalent.
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Binary to Octal Conversion, , A binary number can be converted into its octal equivalent by grouping, binary digits to group of 3 bits and then each group is converted to its octal, equivalent. Start grouping from right to left.
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Qn 9. Convert (111000101)2 to octal
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Binary to Hexa Decimal Conversion, , A binary number can be converted into its hexadecimal by grouping binary, digits to group of 4 bits and then each group is converted to its hexa decimal, equivalent. Start grouping from right to left.
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Qn11. Convert (453)8 to, hexadecimal, , Conversion of an octal number to hexadecimal number is a two step process., Octal number is first converted into binary. This binary equivalent is then, converted into hexadecimal.
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Decimal Fraction to Binary Conversion
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Qn 13. Convert 31.375 to binary
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Binary Fraction to Decimal Conversion, , Qn14 . Convert (1111.011)2 to decimal
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Decimal, , Binary, , 0.5, , 0.1, , 0.25, , 0.01, , 0.125, , 0.001, , 0.0625, , 0.0001, , 0.75, , 0.11, , 0.625, , 0.101, , 0.375, , 0.011
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Binary arithmetic
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Data Representation, Data representation is the method used internally to represent, data in a computer, , Representation of Numbers, Representation of integers, Representation of floating point numbers, Representation of characters, Representation of image ,audio and video
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Representation of integers, Three methods, ●, , Sign and Magnitude representation, , ●, , 1’s complement representation, , ●, , 2’s complement representation, , A word is basically a fixed-sized group of bits, that are handled as a unit by a processor., Number of bits in a word is called word length.
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Sign and Magnitude representation, In this method, first bit from left (MSB) is used for representing sign, of integer and remaining 7-bits are used for representing magnitude, of integer., For negative integers sign bit is 1 and for positive integers sign bit is 0., Magnitude is represented as 7 bit binary equivalent of the integer.
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Represent -44 in Sign and Magnitude method
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1’s Complement representation, , ●, , ●, , ●, , First find the binary of the integer and write it in 8-bit, binary form., If number is negative , find 1’s complement of 8-bit binary, If number is positive , 8-bit binary form itself is the, representation.
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2’s Complement of a binary number
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2’s Complement representation, , ●, , ●, , ●, , First find the binary of the integer and write it in 8-bit, binary form., If number is negative , find 2’s complement of 8-bit binary, If number is positive , 8-bit binary form itself is the, representation.
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2’s Complement is the best method because it can represent more numbers and, there is only one representation for zero
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Representation of floating point numbers, A floating point number consists of an integer part and a fractional part., Floating point notation contains two parts -mantissa and exponent, For example, 25.45 can be written as 0.2545×10 2 , where 0.2545 is the mantissa, and the power 2 is the exponent.
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Representation of characters, ●, , ASCII (American Standard Code for Information Interchange), , ●, , ASCII (Indian Standard Code for Information Interchange), , ●, , EBCDIC(Extended Binary Coded Decimal Interchange Code), , ●, , Unicode(Universal Code)
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ASCII, ●, , Stands for American Standard Code for Information Interchange, , ●, , Uses 7 bits to represent each character in computer memory, , ●, , 7-bit code can represent only 128 characters., , ●, , ●, , For example, ASCII code of A is 65, its binary equivalent in 7-bit, is 1000001., Extended ASCII, which uses 8 bits for each character, can, represent 256 different characters.
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ISCII, ●, , Stands for Indian Standard Code for Information Interchange, , ●, , Uses 8 bits and can represent 256 characters., , ●, , ●, , It was evolved under the Department of Electronics and, adopted by the Bureau of Indian Standards (BIS), Nowadays ISCII has been replaced by Unicode.
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EBCDIC, ●, , Stands for Extended Binary Coded Decimal Interchange Code, , ●, , Uses 8 bits and can represent 256 characters, , ●, , used in computers manufactured by International Business, Machine (IBM).
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Unicode, ●, , ●, , ●, , ●, , Stands for universal code., Unicode originally used 16 bits which can represent up to, 65,536 characters., Unicode can represent characters in almost all written, languages of the world., Using 8-bit ASCII we can represent only 256 characters;, Unicode is resolving this limitation.
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●, , JPEG-Joint Picture Experts Group, , ●, , BMP -Bitmap file format, , ●, , TIFF -Tagged Image File Format, , ●, , GIF -Graphics Interchange Format, , ●, , PNG - Portable (Public) Network Graphic, , ●, , MIDI-Musical Instrument Digital Interface, , ●, , AVI -Audio Video Interleave, , ●, , MPEG- Moving Picture Expert Group
