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1 Chapter 2 Number Systems, Operations, and Codes
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
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
4 Table 2--1
5 Decimal-to-Binary Conversion Sum-of-weight method Binary weights = Binary weights =
6 Repeated division-by-2 method
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
8 Binary Addition = = = =
9 Binary Subtraction = = = = with a borrow of
10 Binary Multiplication 0 0 = 0 0 1 = 0 1 0 = 1 = 1
11 Binary Division Use the same procedure as decimal division
12 Hexadecimal Numbers
13 Binary-to-Hexadecimal Conversion
14 Hexadecimal-to-Binary Conversion
15 Hexadecimal-to-Decimal Conversion
17 Decimal-to-Hexadecimal Conversion
18 Binary Coded Decimal (BCD)
20 Digital Codes and Parity
21 ASCII (American Standard Code for Information Interchange)
22 Parity Method for Error Detection
24 Figure 2--8 The system is in its initial state. Digital System Application
25 Figure 2--9 The system has counted 50 bottles of tablets and is working on the next bottle.
26 Figure The system has just counted its fifty-first bottle of tablets.
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