0 - Number Systems, Conversions, Binary Arithmetic

# 0 - Number Systems, Conversions, Binary Arithmetic -...

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Introduction to Number Systems and conversion

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EEN 304 – Logic Design 1 Number systems When we write a decimal (base 10), we use a positional notation; each digit is multiplied by an appropriate power of 10 depending on its position in the number. Example: 953.78 10 = 9 x 10 2 + 5 x 10 1 + 3 x 10 0 + 7 x 10 -1 + 8 x 10 -2 Any positive integer R(R > 1) can be chosen as the radix or base of a number system. If the base is R, then R digits (0, 1, 2, 3,…, R-1) are used. Example: For base 8, the digits allowed are 0,1,2,3,4,5,6,7. Any number written in positional notation can be expanded in a power series in R: If a number N = (a 4 a 3 a 2 a 1 a 0. a -1 a -2 a -3 ) R N = a 4 x R 4 + a 3 x R 3 + a 2 x R 2 + a 1 x R 1 + a 0 x R 0 + a -1 x R -1 + a -2 x R -2 + a -3 x R -3 Where a i is the coefficient of R i & 0 a i R-1. For bases greater than 10, letters are used to represent digits greater than 9. For example, A = 10 10 B = 11 10 C = 12 10 D = 13 10 E = 14 10 F = 15
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