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Chapter 2

Chapter 2. Number Systems, Operations, and Codes. 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

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Chapter 2

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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 ….105 104 103 102 101 100. 10-1 10-2 10-3 10-4 10-5… 14.2 = 1  101 + 4  100 + 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 ….25 24 23 22 21 20 . 2-1 2-2 2-3 2-4 2-5 … 10111 = 1  24 + 0  23 +1  22 +1  21 + 1  20

  4. Table 2--1

  5. Decimal-to-Binary Conversion • Sum-of-weight method • Binary weights • 128 64 32 16 8 4 2 1 • 357 = 256 + 64 + 32 + 4 + 1 101100101 • Binary weights • 512 256 128 64 32 16 8 4 2 1 • 1937 = 1024 + 512 + 256 + 128 + 16 + 1 11110010001

  6. Repeated division-by-2 method

  7. Converting Decimal fractions to Binary • Using Sum-of-weights • Binary weights • 32 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 = 1 0 -1 with a borrow of 1 1011 -111 100

  10. Binary Multiplication 0  0 = 0 0  1 = 0 1  0 = 0 100110 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. Decimal-to-Hexadecimal Conversion

  17. Binary Coded Decimal (BCD)

  18. Digital Codes and Parity

  19. ASCII (American Standard Code for Information Interchange)

  20. Parity Method for Error Detection

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

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

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

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