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1 Chapter 2 Number Systems, Operations, and Codes

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2 Decimal Numbering System The decimal numbering system has 10 digits 0 through 9 The decimal numbering system has a base of 10 with each position weighted by a factor of 10 … … 14.2 = 1 10 -1

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3 Binary Numbers The binary numbering system has 2 digits 0 and 1 The binary numbering system has a base of 2 with each position weighted by a factor of 2 … … = 1 2 0

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4 Table 2--1

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5 Decimal-to-Binary Conversion Sum-of-weight method Binary weights = Binary weights =

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6 Repeated division-by-2 method

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7 Converting Decimal fractions to Binary Using Sum-of-weights Binary weights = Repeated division by 2 yields the whole number while repeated multiplication by 2 of the fraction yields the binary fraction

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8 Binary Addition = = = =

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9 Binary Subtraction = = = = with a borrow of

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10 Binary Multiplication 0 0 = 0 0 1 = 0 1 0 = 1 = 1

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11 Binary Division Use the same procedure as decimal division

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12 Hexadecimal Numbers

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13 Binary-to-Hexadecimal Conversion

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14 Hexadecimal-to-Binary Conversion

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15 Hexadecimal-to-Decimal Conversion

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17 Decimal-to-Hexadecimal Conversion

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18 Binary Coded Decimal (BCD)

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20 Digital Codes and Parity

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21 ASCII (American Standard Code for Information Interchange)

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22 Parity Method for Error Detection

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24 Figure 2--8 The system is in its initial state. Digital System Application

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25 Figure 2--9 The system has counted 50 bottles of tablets and is working on the next bottle.

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26 Figure The system has just counted its fifty-first bottle of tablets.

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