1. Introduction to Basic Digital Logic
©Paul Godin
Updated December 2014
gmail.com
Presentation 1

2. Digital Electronics

3. Basic Digital Logic Concepts
Digital Systems

4. “Digital” A Digital World What does “Digital” mean?
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. Examples
Measure temperature, a continuous value

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. 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. 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
telephone
communication systems (radio, computer, etc)
sound reproduction
video reproduction
instrumentation
timekeeping
etc

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. Number Systems 5 6 3 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:
Most Significant Digit
(MSD)
Least Significant Digit
(LSD) 5 6 3
5 x x x 100
5 hundreds + 6 tens + 3 ones

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”) on
off
Power switches have labels “1” for on and “0” for off.

12. Binary
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 is 2.
Base 2 = Base 10
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
Binary to Decimal

13. 100101112 Binary digits Bit: single binary digit Byte: 8 binary digits
Radix
Byte

14. Converting Binary to Decimal
Each position represents a numerical “weight”
10112 20 21 22 23
= = 11 in decimal

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

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: (0) to (F)
Easier than using ones and zeros for large binary values
Commonly used in computer applications
Examples:
11002 = 1210 = C16
= A6 C216
Hex values can be followed by an “H” to indicate base-16. Example: A6 C2 H

17. Hex Values in Computers

18. Decimal to Hexadecimal1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F

19. Conversion Binary to Hexadecimal1
1010 = 10
1100 = 12
0001 = 1
0110 = 6 A C 1 6

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’ (10102 to 11112).
00002 to 10012

21. Octal
Octal is a Base-8 numbering system that relates to a 3-bit binary number.
Binary 0002 to 1112 relate directly to numbers 010 to 710
This numbering system is no longer in common use.

22. Conversion Chart Binary BCD Decimal Octal Hex 0000 0001 1 0010 2 0011
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8 10
1001 9 11
1010 x 12 A
1011 13 B
1100 14 C
1101 15 D
1110 16 E
1111 17 F

23. 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.
214=16,364 = 16k
215=32,768 = 32k
216=65,536 = 64k
217=131,072= 128k
218=262,144= 256k
219=524,288= 512k
220=1,048,576= 1M …
Every bit added to the binary number doubles the unique values it can represent

24. Review 1
Define:
Binary
Decimal
Hexadecimal
Convert to:

25. Binary as Electrical Values
Electrical Representation of Binary Values.

26. 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.

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

28. Digital Waveform 1 1 1 Ideal Digital Waveform Logic 1 Logic 0
Waveform to Digital value 1 1 1

29. Analog versus Digital A to A Distorted Analog signal A to D
A to D
Original Analog signal
Binary signal

30. The voltage is converted to a binary value at regular intervals.
Analog to Digital …
Original Analog signal
A to D Conversion
The voltage is converted to a binary value at regular intervals.
Binary signal
Animated

31. The binary value is converted to a voltage at regular intervals.
Digital to Analog …
D to A Conversion
Analog signal
The binary value is converted to a voltage at regular intervals.
Digital signal
Animated

32. 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.

33. 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