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

Digital Electronics

Basic Digital Logic Concepts Digital Systems

“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.

Examples Measure temperature, a continuous value

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.

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)

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

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

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: 56310 Most Significant Digit (MSD) Least Significant Digit (LSD) 5 6 3 5 x 102 + 6 x 101 + 3 x 100 5 hundreds + 6 tens + 3 ones

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.

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 01102 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

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

Converting Binary to Decimal Each position represents a numerical “weight” 10112 20 21 22 23 23+21+20= 8+2+1 = 11 in decimal

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 = 16 + 1 = 17 01111 = 10000 – 1 = 16 -1 = 15 01010 = 8 + 2 = 10

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: 00002 (0) to 11112 (F) Easier than using ones and zeros for large binary values Commonly used in computer applications Examples: 11002 = 1210 = C16 1010 0110 1100 00102 = A6 C216 Hex values can be followed by an “H” to indicate base-16. Example: A6 C2 H

Hex Values in Computers

Decimal to Hexadecimal 1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F

Conversion Binary to Hexadecimal 1 1010 = 10 1100 = 12 0001 = 1 0110 = 6 A C 1 6

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

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.

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

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

Review 1 Define: Binary Decimal Hexadecimal Convert 10102 to:

Binary as Electrical Values Electrical Representation of Binary Values.

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.

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.

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

Analog versus Digital A to A Distorted Analog signal A to D 000000100000010000101000101000011010010011001110101000100000101000101000011010010011001110101000100000001000010100000010000101000101000011010010011001110101000100001010000110100100110011101010001010111011011010001001 A to D Original Analog signal Binary signal

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

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

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.

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