How A Computer Works
1 Learning Objectives
By the end of the lesson…
- All Should Be able to complete the truth table for a NOT gate.
- All Should Be able to describe the function of a NOT gate as an inverter.
- Most Should Know that computer circuits are built from Transistors.
- Most Should Understand the term Boolean Logic (such as AND, OR and NOT).
- Most Should Be able to complete a truth table for a NOR,OR and XOR gate.
- Some Could Evaluate that the output from a gate depends on the pattern of transistors in its circuitry.
- Some Could Explain how a D Latch works in a circuit with two possible stable states.
2 Simplifying NAND gates
Learn It
Let's look at other gates
- NAND gates are really useful, but it would be annoying to have to draw the transistors every time.
- Instead we use a symbol like the one shown below. You can click the buttons and compare it to the transistor version below it, to see that they are identical in function.
3 Combining NAND gates
- NAND gates are said to be universal logical gates because you can make all other types of logic gate out of them.
- We can take a single NAND gate like this one.
- And use it to make this
- This is called an AND gate.
- Here is an online gate builder which is a nice way to visualise what is happening.
4 Assessment
Badge It - Silver
- Have a look at the below. This is the arrangement for a NOT gate, sometimes called an inverter.
- Construct a Truth table for the arrangement, showing input A output Q.
- Describe why the NOT gate is often called an Inverter?
A | Q |
---|---|
0 | |
1 |
5 Making other gates from NAND gates
- We've already seen one other gate that can be made using NAND gates - it was called an AND gate.
- Below is the diagram for the NAND gate arrangements for an AND gate again, and a simplified symbol for an AND gate that is commonly used.
- Hopefully you can see that the two are identical. When inputs A and B are on, output Q is on. When either or both A and B are off, Q is off.
- The AND gate has a very similar symbol to the NAND gate (it's just missing the little circle near the output) so make sure you don't get the two confused.
- The truth table for an AND gate looks like this
A | B | Q |
---|---|---|
0 | 0 | 0 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |
6 Assessment
Badge It - Gold
- Click on this link to watch a short video on the introduction to logic gates.
- Look at the diagrams below, showing other NAND gate arrangements. These are called OR, NOR and XOR gates.
- For each one, draw a Truth Table showing inputs and outputs.
- OR gate
- NOR gate
- XOR gate
7 Assessment
Badge It - Platinum
- There is a special arrangement of NAND gates called a D-Latch.
- Use the Web to find out what the arrangement of NAND gates in a D-Latch is.
- Write a description of a D-Latch and explain why it is useful in computing.