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

16

17 Decimal-to-Hexadecimal Conversion

18 Binary Coded Decimal (BCD)

19

20 Digital Codes and Parity

21 ASCII (American Standard Code for Information Interchange)

22 Parity Method for Error Detection

23

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.