Replace each hexadecimal digit with the corresponding 4-bit binary string 8B16 = 1000 1011 = 100010112 Page 2 Conversion of Decimal Numbers
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[PDF] NUMBER SYSTEM CONVERSIONS - ipsgwaliororg
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 ))
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NUMBER SYSTEM CONVERSION There are many methods or techniques which can be used to convert numbers from one base to another We'll demonstrate
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Uses 16 symbols: 0, 1, 2, , 9, A, B, C, D, E, F Notes: ▫ When written down, a number may be ambiguous regarding which system it belongs to So we will
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for example: we use 10-based numbering system for input and output in digital calculator There are two ways to convert a decimal number to its equivalent quotient of 0 is obtained Note: The binary result is obtained by writing the first
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number system, e g , it may be required to convert a decimal number to binary or octal or hexadecimal The reverse is also true, i e , a binary number may be
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The base or radix of number system determines how many numerical digits the number To convert a decimal number to any other number system, divide the decimal And note down the remainders in the reverse order • To convert from
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Decimal Numbering System Can convert from any base to base 10 Summary Humans think about numbers in decimal; computers think about numbers in
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Replace each hexadecimal digit with the corresponding 4-bit binary string 8B16 = 1000 1011 = 100010112 Page 2 Conversion of Decimal Numbers
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Moreover, we can always convert them from any high-base number system to a Note that since these number systems possess base 2k , all numbers within
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Binary : 7 3 1 Octal : 111011 001 So, 731, = 1110110012 5 Decimal to Octal Conversion: To convert a decimal number to its octal equivalent, the remainder
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Conversion of Binary, Octal and
Hexadecimal Numbers
From Binary to Octal
Starting at the binary point and working left, separate the bits into groups of three and replace each group with the corresponding octal digit.10001011
2 = 010 001 011 = 2138
From Binary to Hexadecimal
Starting at the binary point and working left, separate the bits into groups of four and replace each group with the corresponding hexadecimal digit.10001011
2 = 1000 1011 = 8B16
From Octal to Binary
Replace each octal digit with the corresponding 3-bit binary string. 2138 = 010 001 011 = 100010112
From Hexadecimal to Binary
Replace each hexadecimal digit with the corresponding 4-bit binary string. 8B16 = 1000 1011 = 100010112
Conversion of Decimal Numbers
From Decimal to Binary
171234026912139128024022021MSDLSD
From Binary to Decimal
10001011
2 = 1´27 + 0´26 + 0´25 + 0´24 + 1´23 + 0´22 + 1´21 + 1´20 = 128 + 8 + 2 + 113910 = 100010112
Conversion of Fractions
Starting at the binary point, group the binary digits that lie to the right into groups of three or four.0.10111
2 = 0.101 110 = 0.568
0.1011
2 = 0.1011 1000 = 0.B816
ProblemsConvert the following
BinaryOctalDecimalHex10011010
27052705
3BC