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1 Chapter 2 Number Systems, Operations, and Codes.

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Presentation on theme: "1 Chapter 2 Number Systems, Operations, and Codes."— Presentation transcript:

1 1 Chapter 2 Number Systems, Operations, and Codes

2 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 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 4 Table 2--1

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

6 6 Repeated division-by-2 method

7 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 8 Binary Addition = = = =

9 9 Binary Subtraction = = = = with a borrow of

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

11 11 Binary Division Use the same procedure as decimal division

12 12 Hexadecimal Numbers

13 13 Binary-to-Hexadecimal Conversion

14 14 Hexadecimal-to-Binary Conversion

15 15 Hexadecimal-to-Decimal Conversion

16 16

17 17 Decimal-to-Hexadecimal Conversion

18 18 Binary Coded Decimal (BCD)

19 19

20 20 Digital Codes and Parity

21 21 ASCII (American Standard Code for Information Interchange)

22 22 Parity Method for Error Detection

23 23

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

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

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


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