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# DECIMAL, BINARY, AND HEXADECIMAL - University of … - converting a number to binary

DECIMAL, BINARY, AND
Decimal Numbering System
Ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Represent larger numbers as a sequence of digits
? Each digit is one of the available symbols
Example: 7061 in decimal (base 10)
? 706110 = (7 x 103) + (0 x 102) + (6 x 101) + (1 x 100)
Octal Numbering System
Eight symbols: : 0, 1, 2, 3, 4, 5, 6, 7
? Notice that we no longer use 8 or 9
Base Comparison:
Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...
Base 8: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14...
Example: What is 158 in base 10?
? 158 = (1 x 81) + (5 x 80) = 1310
Example: What is 70618 in base 10?
? 70618 = (7 x 83) + (0 x 82) + (6 x 81) + (1 x 80) = 363310

How do you change numbers to binary? To convert a decimal number to binary floating point representation: Convert the absolute value of the decimal number to a binary integer plus a binary fraction. Normalize the number in binary scientific notation to obtain m and e. Set s=0 for a positive number and s=1 for a negative number.

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