Presentation is loading. Please wait.

# 1 Chapter 2 Number Systems, Operations, and Codes.

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

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 ….10 5 10 4 10 3 10 2 10 1 10 0. 10 -1 10 -2 10 -3 10 -4 10 -5 … 14.2 = 1  10 1 + 4  10 0 + 2  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 ….2 5 2 4 2 3 2 2 2 1 2 0. 2 -1 2 -2 2 -3 2 -4 2 -5 … 10111 = 1  2 4 + 0  2 3 +1  2 2 +1  2 1 + 1  2 0

4 Table 2--1

5 Decimal-to-Binary Conversion Sum-of-weight method Binary weights 256 128 64 32 16 8 4 2 1 357 = 256 + 64 + 32 + 4 + 1 101100101 Binary weights 1024 512 256 128 64 32 16 8 4 2 1 1937 = 1024 + 512 + 256 + 128 + 16 + 111110010001

6 Repeated division-by-2 method

7 Converting Decimal fractions to Binary Using Sum-of-weights Binary weights 6432 16 8 4 2 1.5.25.125.0625 95.6875 = 64 + 16 + 8 + 4 + 2 + 1 +.5 +.125 +.0625 1011111.1011 Repeated division by 2 yields the whole number while repeated multiplication by 2 of the fraction yields the binary fraction

8 Binary Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 11001 +1101 100110

9 Binary Subtraction 0 - 0 = 0 1 - 1 = 0 1 - 0 = 1 10 -1 = 10 -1 with a borrow of 1 1011 -111 100

10 Binary Multiplication 0  0 = 0 0  1 = 0 1  0 = 0100110 1  1 = 1  101 100110 000000 100110 10111110

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 2--10 The system has just counted its fifty-first bottle of tablets.

Download ppt "1 Chapter 2 Number Systems, Operations, and Codes."

Similar presentations

Ads by Google