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9.9 Option - The Age of Silicon: 5. Circuits and information processing
| Syllabus reference (October 2002 version) | ||
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5.Information can be processed using electronic
circuits
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Students learn to: | Students: |
Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 21 Aug 08]
describe the behaviour of AND, OR and inverter logic gates in terms of high and low voltages and relate these to input and outputs
- Logic is a form of human reasoning that tells
us a certain proposition is true if certain
preconditions are true.
- In 1854 George Boole developed a mathematical system
for formulating logic statements with symbols, so the
problems could be written and solved in a similar manner to
ordinary algebra. His system is called Boolean Algebra and
it is used in the analysis and design of digital systems.
- The basic building blocks of digital circuits are
called logic gates. A gate is a circuit that performs a
simple logic operation. Gates can have one, two, three or
more inputs and the basic gates have a single output
dependent on the inputs. Each output is also called a
digital ‘bit’ of information (or
‘bit’ for short).
- The behavior of a gate can be shown in a truth table which systematically lists all the possible input states for a gate and the corresponding output states. Gates can be represented in five ways.
Consider the AND gate:
- A zero ( 0 ) corresponds to a low voltage. A one ( 1 ) corresponds to a high voltage. An inverter logic gates converts a low voltage ( 0 ) to a high voltage ( 1 ) or vice versa. Some alternative meanings for 0 and 1 are as follows:
| Logic 0 | Logic 1 |
|---|---|
| False | True |
| Off | On |
| High | Low |
| Open switch | Closed switch |
- Digital circuits can be put together using diodes, transistors and resistors and connected together to provide a circuit output that corresponds to the logic operations OR, AND, NOT performed on the inputs to those circuits.
- NOR and
NAND
gates are used extensively in
digital circuitry. These gates combine the basic operations
AND
OR and
NOT which make it relatively easy to
describe them using Boolean Algebra. EELAB Student Pages,
Electrical and Information Engineering, The University of
Sydney, NSW.
- In working through the above information about logic
gates, you will have noticed that each logic gate is
represented uniquely. This is useful when drawing and
interpreting diagrams of logic circuits.
The set of symbols is as follows:
| Name | Symbol | Input | Output |
|---|---|---|---|
| AND |  |
Two signals | One signal |
| OR |  |
Two signals | One signal |
| NOT |  |
One signal | One signal |
| NAND |  |
Two signals | One signal |
| NOR |  |
Two signals | One signal |
| XOR |  |
Two signals | One signal |
identify that gates can be used in combination with each other to make half or full adders
- Practical circuits to perform arithmetic operations,
such as addition, combine two or more gates in a circuit to
provide a result.
- Two such circuits are the half-adder and full-adder. In the examples below, a bit represents the binary digits 1 or 0.
A half-adder
The need for two outputs to represent the sum of two binary 1s is obvious:
1 + 1 = 1 0
This is not ten, but two. The two digits are distinguished by their place or position relative to each other. The left-most digit is the significant bit (and is assigned the C for carry label); the right-most digit is the least significant bit (and is assigned the S for sum label).
A combination of gates in a circuit that adds two bits is called a half-adder. In the above case, this is achieved by combining an exclusive-OR and an AND gate.
A combination of gates in a circuit to add three bits is called a full-adder. The circuit below shows a combination of gates to produce a full-adder. A and B are the two inputs for this operation. CI (the third input digit) is the least significant bit from the two outputs of a separate half-adder circuit.
The term significant or least significant in front of 'bit' is necessary in order to correctly sequence the digits that represent the sum from the operation of the gates in the circuit. If all three inputs are carrying a 1, then the sum is 3 (the 1 from CI is the least significant bit from the other circuit). This is represented in binary code as 11 (see the truth table for the full-adder).
A full-adder
identify data sources, plan, choose equipment or resources for, and perform first-hand investigations to construct truth tables for logic gates
- Use your own resources to draw circuit diagrams and truth tables to represent a three input OR gate (can you use a NOR gate and another gate to achieve the same result?).
- Use your own resources to draw circuit diagrams and truth tables to represent a three input AND gate.
solve problems and analyse information using circuit diagrams involving logic gates
-
Do this question from the
2003 HSC paper (Q 32. Scroll down to
p 41 to find the question.)
-
Do this question from the
2004 HSC paper (Q 32 (b). Scroll
down to p 37.)
Truth table
| A | B | C | D | E | What is X | Output |
|---|---|---|---|---|---|---|
| 1 | 1 | ? | ? | ? | ? | 1 |
Is there only one answer to X? Explain your answer.
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