# NUMBERS - Binary Number Systems and Codes ECEn 220 02...

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© 2003-2014 BYU 02 NUMBERS Page 1 ECEn 220 Binary Number Systems and Codes

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© 2003-2014 BYU 02 NUMBERS Page 2 ECEn 220 Positional Numbers What does 5132.13 really mean? Depends on the number base! Assuming base 10: 5132.13 10 = 5 x10 3 + 1 x10 2 + 3 x10 1 + 2 x10 0 + 1 x10 -1 + 3 x10 -2 Assuming base 6: 5132.13 6 = 5 x6 3 + 1 x6 2 + 3 x6 1 + 2 x6 0 + 1 x6 -1 + 3 x6 -2 We often use a subscript to indicate the base.
© 2003-2014 BYU 02 NUMBERS Page 3 ECEn 220 Positional Number Examples 527.46 10 = (5 x 10 2 ) + (2 x 10 1 ) + (7 x 10 0 ) + (4 x 10 -1 ) + (6 x 10 -2 ) 527.46 8 = (5 x 8 2 ) + (2 x 8 1 ) + (7 x 8 0 ) + (4 x 8 -1 ) + (6 x 8 -2 ) 527.46 5 = illegal why? 1011.11 2 = (1 x 2 3 ) + (0 x 2 2 ) + (1 x 2 1 ) + (1 x 2 0 ) + (1 x 2 -1 ) + (1 x 2 -2 ) This works for binary as well…

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© 2003-2014 BYU 02 NUMBERS Page 4 ECEn 220 Conversion from Binary Convert 101011.11 2 to base 10: 101011.11 2 = 1x2 5 + 0x2 4 + 1x2 3 + 0x2 2 + 1x2 1 + 1x2 0 + 1x2 -1 + 1x2 -2 = 32 + 0 + 8 + 0 + 2 + 1 + ½ + ¼ = 43.75 10
© 2003-2014 BYU 02 NUMBERS Page 5 ECEn 220 Convert 114 10 to binary: 114 50 18 2 - 64 1x2 6 - 32 1x2 5 - 16 1x2 4 2 - 0 0x2 3 2 - 0 0x2 2 0 - 2 1x2 1 - 0 0x2 0 0 114 10 = 1110010 2 Read this way This method also works for fractional numbers.

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© 2003-2014 BYU 02 NUMBERS Page 6 ECEn 220 114 An Alternate Method 2 2 2 2 2 2 2 57 R 0 28 R 1 14 R 0 7 R 0 3 R 1 1 R 1 0 R 1 114 10 = 1110010 2 Read this way
© 2003-2014 BYU 02 NUMBERS Page 7 ECEn 220 Converting fractions from base 10 to binary: Convert 0.7

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• Fall '13
• Binary numeral system, ASCII, ECEN

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