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DECIMAL TO OTHER, 1. DECIMAL TO BINARY, 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 Conversion, Decimal Number is : (12345)10, , Result, , Binary Number is, (11000000111001)2, , 2. DECIMAL TO OCTAL, Decimal to Octal Conversion Result, Decimal Number is : (12345)10, Octal Number is, (30071)8, , 3. DECIMAL TO HEXADECIMAL

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Decimal to Hexadecimal Conversion, Example 1, Decimal Number is : (12345)10, , Result, , Hexadecimal Number is, (3039)16, , Example 2, Decimal Number is : (725)10, , Hexadecimal Number is, (2D5)16, Convert, 10, 11, 12, 13, 14, 15, to its equivalent..., A, B, C, D, E, F, , BINARY TO OTHER, A) Multiply the digit with 2(with place value exponent). Eventually add all the multiplication, becomes the Decimal number., 1. BINARY TO DECIMAL, , 2. BINARY TO OCTAL, An easy way to convert from binary to octal is to group binary digits into sets of three, starting, with the least significant (rightmost) digits., Binary: 11100101 = 11 100 101, 011 100 101 Pad the most significant digits with zeros if, necessary to complete a group of three., Then, look up each group in a table:, Binary:, , 000, , 001, , 010, , 011, , 100, , 101, , 110, , 111

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Octal:, , 0, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , Binary = 011 100 101, Octal =, 3 4 5 = 345 oct, , 3. BINARY TO HEXADECIMAL, An equally easy way to convert from binary to hexadecimal is to group binary digits into sets of, four, starting with the least significant (rightmost) digits., Binary: 11100101 = 1110, , 0101, , Then, look up each group in a table:, Binary:, , 0000 0001 0010 0011 0100 0101 0110 0111, , Hexadecimal:, , 0, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , Binary:, 1000 1001 1010 1011 1100 1101 1110 1111, Hexadecimal: 8, 9, A, B, C, D, E, F, Binary =, 1110 0101, Hexadecimal =, E, 5 = E5 hex, , OCTAL TO OTHER, 1. OCTAL TO BINARY, Converting from octal to binary is as easy as converting from binary to octal. Simply look up, each octal digit to obtain the equivalent group of three binary digits., Octal: 0 1 2 3 4 5 6 7, Binary: 000 001 010 011 100 101 110 111, Octal =, 3 4 5, Binary = 011 100 101 = 011100101 binary, , 2. OCTAL TO HEXADECIMAL, When converting from octal to hexadecimal, it is often easier to first convert the octal number, into binary and then from binary into hexadecimal. For example, to convert 345 octal into hex:, (from the previous example), Octal =, , 3, , 4, , 5, , Binary = 011 100 101 = 011100101 binary

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Drop any leading zeros or pad with leading zeros to get groups of four binary digits (bits):, Binary 011100101 = 1110 0101, Then, look up the groups in a table to convert to hexadecimal digits., Binary:, , 0000 0001 0010 0011 0100 0101 0110 0111, , Hexadecimal: 0, , Binary:, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , 1000 1001 1010 1011 1100 1101 1110 1111, , Hexadecimal: 8, , Binary =, Hexadecimal =, , 9, , A, , B, , C, , D, , E, , F, , 1110 0101, E, , 5 = E5 hex, , Therefore, through a two-step conversion process, octal 345 equals binary 011100101 equals, hexadecimal E5., , 3. OCTAL TO DECIMAL, The conversion can also be performed in the conventional mathematical way, by showing each, digit place as an increasing power of 8., 345 octal = (3 * 82) + (4 * 81) + (5 * 80) = (3 * 64) + (4 * 8) + (5 * 1) = 229 decimal, OR, Converting octal to decimal can be done with repeated division., 1., 2., 3., 4., 5., , Start the decimal result at 0., Remove the most significant octal digit (leftmost) and add it to the result., If all octal digits have been removed, you’re done. Stop., Otherwise, multiply the result by 8., Go to step 2., , Octal Digits Operation Decimal Result Operation Decimal Result, 345, +3, 3, ×8, 24, 45, +4, 28, ×8, 224, 5, +5, 229, done.

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, , (345)8 =(229)10, , HEXADECIMAL TO OTHER, 1. HEXADECIMAL TO BINARY, Converting from hexadecimal to binary is as easy as converting from binary to hexadecimal., Simply look up each hexadecimal digit to obtain the equivalent group of four binary digits., Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, Binary:, 0000 0001 0010 0011 0100 0101 0110 0111, Hexadecimal: 8, 9, A, B, C, D, E, F, Binary:, 1000 1001 1010 1011 1100 1101 1110 1111, Hexadecimal =, A, 2, D, E, Binary =, 1010 0010 1101 1110 = 1010001011011110 binary, 2. HEXADECIMAL TO OCTAL

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

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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, , 2'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, Example of 2's Complement is as follows.

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Rules of Binary Addition, , , , , , 0, 0, 1, 1, , +, +, +, +, , 0, 1, 0, 1, , =, =, =, =, , 0, 1, 1, 0,, , and carry 1 to the next more significant bit, , For example,, 00011010 + 00001100 = 00100110, 0, + 0, , 0, 0, , 1, 0, 0, , 1, 1, 0, , 1, 1, , 0, 1, , 1, 0, , 0, 0, , Carries, = 26(base 10), = 12(base 10), , 0, , 0, , 1, , 0, , 0, , 1, , 1, , 0, , = 38(base 10), , 0, + 0, , 1, 0, 0, , 1, 0, 1, , 1, 1, 1, , 1, 0, 1, , 1, 0, 1, , 1, 1, , 1, 0, , carries, = 19(base 10), = 62(base 10), , 0, , 1, , 0, , 1, , 0, , 0, , 0, , 1, , = 81(base 10), , 00010011 + 00111110 = 01010001, , Rules of Binary Multiplication, , , , , , 0, 0, 1, 1, , x, x, x, x, , 0, 1, 0, 1, , =, =, =, =, , 0, 0, 0, 1,, , and no carry or borrow bits, , For example,, 00101001 × 00000110 = 11110110, , 0, × 0, , 0, 0, , 1, 0, , 0, 0, , 1, 0, , 0, 1, , 0, 1, , 1, 0, , 0, 1, 0, , 0, 0, 1, , 0, 1, 0, , 0, 0, 0, , 0, 0, 1, , 0, 1, , 0, , 0, 0, 1, , 0, , 0, 0, , 0, , 0, , 1, , 1, , 1, , 1, , 0, , 1, , 1, , 0, , =, =, , 41(base 10), 6(base 10), , = 246(base 10), , Binary Division, Binary division is the repeated process of subtraction, just as in decimal division., For example,, 00101010 ÷ 00000110 =, , 1, , 1, , 1, , =, , 7(base 10)

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00000111, 1, , 1, , 0, , ), , 0, , 0, , 1, , 1, , 0, , 1, , 0, , 1, , 1, , 0, , -, , 1, , 0, , =, =, , 1, 1, , 0, 1, , -, , -, , 42(base 10), 6(base 10), borrows, , 1, , 0, 1, , 1, 0, , 1, 1, , 1, 1, , 0, 0, 0, , 10000111 ÷ 00000101 =, 00011011, 1, , 0, , 1, , ), , 1, -, , -, , 1, , 1, , 0, , 1, , 1, , =, , 0, , 0, , 1, , 1, , 1, , =, , 1, , 0, , 0, , 1, , 0, , 1, , 1, 1, , 1, 0, , 135(base, 10), , =, 1, , 0, 1, 1, , 1, 0, , 1, 1, , 1, 0, , 1, 1, , 1, 1, , 0, 0, , -, , -, , -, , 1, 1, 0, , Example − Division, , 27(base 10), , 5(base 10)