2. Digital Electronics

3. Chapter 1 Binary Systems

4. Digital Electronics Galore! Digital Cameras Digital Versatile Disks (DVD) Digital Computers Digital Televisions Digital Telephones Digital Birthday Cards

5. Binary Numbers 10 3 10 2 10 1 10 0 7 5 8 3 1 1 0 1 2 3 2 2 2 1 2 0 Decimal Binary

6. Binary Drill 1101 = ? 1001 = ? 1000 = ? 0101 = ? 1010 = ?

7. Binary Drill … Solutions 1101 = 13 1001 = 9 1000 = 8 0101 = 5 1010 = 10

8. Hexadecimal (Base 16) 16 3 16 2 16 1 16 0 So 38 16 = what in decimal?

9. Hexadecimal Solution 38 16 = 56 10

10. Decimal - Hexadecimal 0 through 9 = 0 through 9 10 = A 11 = B 12 = C 13 = D 14 = E 15 = F 16 = 10 17 = 11 18 = 12

11. Hexadecimal Drill 2B7 = what in decimal? Hint: Think … 16 3 16 2 16 1 16 0

12. Hexadecimal Drill … Solution 2B7 = 256 x 2 + 16 x 11 + 7 Hint: Think … 16 3 16 2 16 1 16 0 2B7 16 = 695 10

13. Hexadecimal To Binary 2B7 = what in binary? Hint Secret Recipe: Convert digit by digit!!!

14. Hex2Bin … Solution 2B7 = what in binary? Secret Recipe: Convert digit by digit!!! 2 B 7 16 = 0010 1011 0111

15. Octal (Base 8) 8 3 8 2 8 1 8 0 So 65 8 = what in decimal?

16. Octal Solution 65 8 = 53 10

17. Decimal - Octal 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 8 = 10 9 = 11 10 = 12

18. Octal Drill 217 8 = what in decimal? Hint: Think … 8 3 8 2 8 1 8 0

19. Octal Drill … Solution 217 8 = 64 x 2 + 8 x 1 + 7 217 8 = 143 10 Hint: Think … 8 3 8 2 8 1 8 0

20. Octal To Binary 217 8 = what in binary? Hint : Groups of 3 Secret Recipe: Convert digit by digit!!!

21. Oct2Bin … Solution 217 = what in binary? Secret Recipe: Convert digit by digit!!! 2 1 7 8 = 010 001 111

22. Fractions in Binary 21.75 = what in binary? 2 1.75 10 = 10101. 11 2 3 2 2 2 1 2 0. 2 -1 2 -2 2 -3

23. Fractions … Drill 41.6875 = what in binary? 2 3 2 2 2 1 2 0. 2 -1 2 -2 2 -3

24. Fractions … Drill 41.6875 10 = 101001.1011 2 3 2 2 2 1 2 0. 2 -1 2 -2 2 -3

25. Complements 1’s complement is formed by inverting the digits 1’s complement of 10010001 = 01101110 2’s complement is formed by adding 1 to the 1’s complement 2’s complement of 10010001 = 01101111

26. Negative (signed) Numbers 2’s complement is used to represent a negative number Example: 117 - 102 115 = 01110011 and 102 = 01100110 So -102 = 10011010 So 115 = 01110011 -102 = 10011010 13 = 00001101

27. BCD (Binary Coded Decimal) Example 875 10 = 1000 0111 0101 Note that each digit is coded individually. Do not confuse this with pure binary!

28. ASCII Character Codes CAPS:A = 41 16 = 1000001 G = 47 16 = 1000010 Z = 5A 16 = 1011010 lower casea = 61 16 = 1100001 h = 68 16 = 0111000 z = 7A 16 = 1111010 digits 0 -9 4 = 34 16 = 0110100 8 = 38 16 = 0111000

29. Error Detection and Parity Parity bit is an extra bit added to make the total number of 1’s even or odd depending on the protocol agreed upon A with even parity = 01000001 A with odd parity = 11000001 Parity bit helps in detecting errors during transmission.

30. Binary Logic AND means ALL conditions must be TRUE for the outcome to be true. For instance, you must study AND take the test in order to pass this class. OR means AT LEAST ONE condition must be true for the outcome to be true. For instance, you can walk, ride the bike, or drive to get to school.

31. Logic Gates ANDOR xy x  y xy x+y 000000 010011 100101 111111

32. Digital Logic Gates AND OR NOT

33. Timing Diagrams

34. That’s All Folks!