Intro to Digital Logic

What does “Digital” mean?• A method of storing, processing and

transmitting information through the use of distinct electronic or optical pulses that typically represent the binary digits 0 and 1.

• This is typically represented by transistors switched “on” or “off”

• Data carrying signals carry one of two possible values.

• 1/0,on/off,high/low, or pulse present/pulse absent

What was the earliest digital communication?

• Morse code?

• Does it have different states?

• 5 different states, but still digital

• Semaphore?

• What about smoke signals?

• One if by air, two if by sea?

• All digital, as they are using a code to represent a message

Logic!

• Why is this unit called digital logic?

• What is logic?

• Logic in these gates is based on theories from a book called “An investigation in the laws of thought” by George Boole.

• This came to be known as Boolean Logic or Boolean Algebra

Thoughts

• There IS a transition between the low and high, and back to low signals.

• In the ideal setting, there would be no transition.

• Real world circuits approximate this well enough that we will not take it into consideration

Gates

• There are seven gates.• The first two are AND and OR gates

AND gate

• The AND gate logic is such that BOTH outputs must be high to trigger a high output

• This is like two doors in a row that both must be open to pass a beam of light through

The switch analogy

• We can build a manual approximation of the circuit using switches very easily.

The OR gate

• The OR gate is such that when a high signal is sent on either input, the output will be high.

• This is like a double door that either side can open to let the light through.

The switch analogy

• We can build a manual approximation of the circuit using switches very easily.

Positive Logic Vs Negative Logic

Positive Logic Vs. Negative Logic

• When describing the input states, we can use positive or negative logic

• For example, the AND gate:

• Positive Logic

• When both inputs are high, the output is high

• Negative Logic

• When either input is low, the output is low

Interesting coincidence• On the and gate:• If either input 1 OR input 2 are low, the

output is low• OR? How did OR get in there?• This Positive AND gate is also a Negative

OR gate!• On an OR gate, both input 1 AND input 2

have to be low in order to have a low output!• AND!?• A positive OR gate is a Negative AND gate!

Truth Table (or trooth, if you rather)

• A truth table is helpful in determining what type of gate you have, or what you should expect based on your gate

• A and B represent the two inputs

• C represents output• What type of gate is this?

Lab Time

Materials

• Power Supply (Use +5V DC)• Digital Display Module• Bread Board• Interface Module 2• Data Switches• Quad AND Gate• Quad OR Gate• Ribbon Cable• Power Supply Leads• Wire

How to set it up

• Plug the AND gates and Data switches together so they share a common strip in between.

• Plug in the Interface Module 2 in above the 2 other modules.

• Run a ground wire from the ground side of the AND gate to the ground on the Interface Module.

• Plug on end of the ribbon cable into the Interface Module and the other into the DDM on J2

• Turn on power supply and set to +5v DC and hook the leads to the + and – side of the circuit.

Build a Single AND Gate

Build a truth table for this circuit

Build a two AND Gate Circuit

Build a truth table for this circuit

Build a three AND Gate Circuit

Build a truth table for this circuit

Build a Single OR Gate

Build a truth table for this circuit

Build a two OR Gate Circuit

Build a truth table for this circuit

Build a circuit with one AND and one OR

Build a truth table for this circuit