1. 1.1 Introduction to Basic Digital Logic ©Paul Godin Updated August 2014 prgodin @ gmail.com Presentation 1

2. 1.2 Digital Electronics

3. 1.3 Basic Digital Logic Concepts Digital Number System

4. 1.4 “Digital” ◊A Digital World ◊Many of the things we use every day are “digital” or “digitized”. ◊What does “Digital” mean? ◊Represented by discrete (stepped) or numerical values rather than analog (continuous) values.

5. 1.5 Examples Measure temperature, a continuous value

6. 1.6 Advantages of Digital Systems/Values ◊Relatively less sensitive to distortion (noise and losses) ◊Can be reproduced more accurately ◊Easier to reconstruct a signal ◊More storage and transfer options ◊Can be processed mathematically and logically ◊Easier to standardize ◊Systems are easier to design electrically (lower voltage / very low current) ◊Digital systems can be made small ◊Encryption available Many of these concepts will make sense as we progress through this course.

7. 1.7 Disadvantages of Digital Systems/Values ◊Takes time to convert and process values ◊Digital systems have significant electrical limitations (cannot handle large current or high voltage) ◊Can become quite complex with an increase of significant digits ◊Not a completely accurate representation of analog values (rounding errors) ◊Often need to convert to / from analog systems ◊More complex circuitry ◊More sensitive to environmental issues (noise, electrical, temperature, etc)

8. 1.8 Future of Digital Systems ◊With advances in semiconductor manufacturing, digital systems are inexpensive, faster and more complex. ◊In a mass production society the advantages of digital systems outweigh the disadvantages. ◊Digital technology will continue to replace what was typically the analog or mechanical domain. Examples include telephone and other communication systems, broadcast television, sound and video reproduction, instrumentation, timekeeping, etc...

9. 1.9 Basic Digital Logic Concepts Number Systems There are 10 types of people in the world: Those who understand binary, and those who don’t.

10. 1.10 Number Systems We use decimal, or “base-10”. ◊10 digits (0 to 9) The decimal numbering system has positional weighing where each position has a power of 10. Example: 563 10 563 5 x 10 2 + 6 x 10 1 + 3 x 10 0 Most Significant Digit (MSD) Least Significant Digit (LSD) 5 hundreds + 6 tens + 3 ones

11. 1.11 Binary Signals ◊Decimal values are difficult to represent in electrical systems. It is easier to use two voltage values than ten. ◊Binary Signals have two basic states: ◊A good example of binary states is a light (only on or off) 1 (logic “high”, or H, or “on”, or “True”) 0 (logic “low”, or L, or “off”, or “False”) onoff

12. 1.12 Binary Base 2 = Base 10 0000 = 0 0001 = 1 0010 = 2 0011 = 3 0100 = 4 0101 = 5 0110 = 6 0111 = 7 1000 = 8 1001 = 9 In Binary there are only 0’s and 1’s. These numbers are called “Base-2”. The base value is the number of digits in the counting system. It is also known as the radix. Example: the radix of 0110 2 is 2. Binary to Decimal

13. 1.13 Binary digits Bit: single binary digit Byte: 8 binary digits 10010111 2 Bit Byte Radix

14. 1.14 Converting Binary to Decimal Each position represents a numerical “weight” 1011 2 2020 2121 2 2323 2 3 +2 1 +2 0 = 8+2+1 = 11 in decimal

15. Easy Conversion from Binary ◊The easiest way to convert from binary to decimal is to remember the positional values: 1.15 Base 2 = Base 10 00000 = 0 00001 = 1 00010 = 2 00100 = 4 01000 = 8 10000 = 16 10001 = 16 + 1 = 17 01111 = 10000 – 1 = 16 -1 = 15 01010 = 8 + 2 = 10

16. 1.16 Hexadecimal ◊Hexadecimal is used to simplify dealing with large binary values: ◊Base-16, or Hexadecimal, has 16 characters: 0-9, A-F ◊Represent a 4-bit binary value: 0000 2 (0) to 1111 2 (F) ◊Easier than using ones and zeros for large binary values ◊Commonly used in computer applications ◊Examples: ◊1100 2 = 12 10 = C 16 ◊1010 0110 1100 0010 2 = A6 C2 16 Hex values can be followed by an “H” to indicate base-16. Example: A6 C2 H

17. Hex Values in Computers 1.17

18. Decimal to Hexadecimal 1.18 DecimalHex 00 11 22 33 44 55 66 77 88 99 10A 11B 12C 13D 14E 15F

19. Conversion Binary to Hexadecimal 1.19 1010110000010110 1010 = 101100 = 120001 = 10110 = 6 AC16

20. 1.20 BCD ◊BCD (Binary-Coded Decimal) values are used to represent a decimal value in binary. ◊BCD values allow for the easy conversion from binary to decimal. ◊Exclude values beyond ‘9’ (1010 2 to 1111 2 ). ◊0000 2 to 1001 2

21. 1.21 Conversion Chart BinaryBCDDecimalOctalHex 00000000 00011111 00102222 00113333 01004444 01015555 01106666 01117777 100088x8 100199x9 1010x10xA 1011x11xB 1100x12xC 1101x13xD 1110x14xE 1111x15xF

22. 1.22 Binary in everyday life Ever wonder why computer-related values seem to follow a pattern of: 32, 64, 128, 256, 512,…? It is because they are related to binary values. 2 14 =16,364 = 16k 2 15 =32,768 = 32k 2 16 =65,536 = 64k 2 17 =131,072= 128k 2 18 =262,144= 256k 2 19 =524,288= 512k 2 20 =1,048,576= 1M … Every bit added to the binary number doubles the unique values it can represent

23. 1.23 Review 1 ◊Define: ◊Binary ◊Decimal ◊Hexadecimal ◊Convert 1010 2 to: ◊Decimal ◊Hexadecimal

24. 1.24 Binary as Electrical Values Electrical Representation of Binary Values.

25. 1.25 Binary as a Voltage Voltages are used to represent logic values: A voltage present (called Vcc or Vdd) = 1 Zero Volts or ground (called gnd or Vss) = 0 The voltage for a popular family of devices is 5 Volts. Many digital device families function at other voltages.

26. 1.26 A Simple Switch A simple switch provides a logic value: Vcc Gnd, or 0 Vcc Vcc, or 1 There are other, better ways to connect a switch in digital circuits.

27. 1.27 Digital Waveform Logic 1 Logic 0 Ideal Digital Waveform 000111 Waveform to Digital value

28. 1.28 Analog versus Digital 000000100000010000101000 101000011010010011001110 101000100000101000101000 011010010011001110101000 100000001000010100000010 000101000101000011010010 011001110101000100001010 000110100100110011101010 001010111011011010001001 Original Analog signal Distorted Analog signal Binary signal A to A A to D

29. 1.29 Analog to Digital Original Analog signal Binary signal A to D Conversion 000100110111101010001 000111000000100000010 011100101001001011101 011110010101010010101 010101001001010101001 000101001010101111010 000001001011101011101 000000010101110101010 000000000001001111010 000000000000111111010 000000000001010101010 000000000001011011101 000000000001101101100 000000001100010111010 000000100011111010110 000001001010101000100 000001010111101111000 000011001101010100101 000110111000010100101 … The voltage is converted to a binary value at regular intervals. Animated

30. 1.30 Digital to Analog Digital signal Analog signal D to A Conversion 000100110111101010001 000111000000100000010 011100101001001011101 011110010101010010101 010101001001010101001 000101001010101111010 000001001011101011101 000000010101110101010 000000000001001111010 000000000000111111010 000000000001010101010 000000000001011011101 000000000001101101100 000000001100010111010 000000100011111010110 000001001010101000100 000001010111101111000 000011001101010100101 000110111000010100101 … The binary value is converted to a voltage at regular intervals. Animated

31. 1.31 Parallel versus Serial ◊Serial communications: provides a binary number as a sequence of binary digits, one after another, through one data line. ◊Parallel communications: provides a binary number as binary digits through multiple data lines at the same time.

32. 1.32 Exercise ◊Name some advantages of digital signals over analog signals. ◊Discussion: Why have today’s standards gone toward serial communications instead of parallel communications? END