Logic Circuits – JSS3 Computer Studies Lesson Note (Second Term)

What is a logic gate?

A logic gate is an elementary building block of a digital circuit that reads binary inputs and gives one binary output.

• Inputs: most logic gates have two inputs. The NOT gate has only one.
• Output: every logic gate has one output.
• Rule: the gate reads the state of its inputs and sets its output according to its own rule.
• Where found: logic gates are packed into digital integrated circuits (ICs) in computers, phones and calculators.

Behavioural objectives

By the end of the lesson, students should be able to:

1. define a logic gate;
2. list the seven basic logic gates;
3. state when the output of the AND, OR, XOR, NAND, NOR and XNOR gates is “True”;
4. explain what a NOT gate does;
5. state the uses of standard logic circuits.

What are the binary states of a logic gate?

Every input and output of a logic gate is in one of two binary states: low (0) or high (1).

• Low (0): a low voltage, approximately 0V in most gates. It also means “False”.
• High (1): a higher voltage, approximately 5V in most gates. It also means “True”.
• Other ranges: some gates use different voltage levels for low and high.

What is a truth table?

A truth table is a table that lists every possible combination of inputs to a gate and the output each one gives.

• Columns: one column for each input (A and B) and one for the output.
• Rows: a two-input gate has four rows, because two inputs give four combinations.
• Values: 0 stands for “False” and 1 stands for “True”.

What are the seven basic logic gates?

There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR and XNOR.

What is the AND gate?

The AND gate gives “True” only when both inputs are “True”.

• Rule: it acts in the same way as the logical word “AND”.
• True output: when both inputs are 1 (high).
• False output: in every other case.

What is the OR gate?

The OR gate gives “True” when either or both inputs are “True”.

• Rule: it behaves like the logical inclusive “OR”.
• True output: when at least one input is 1.
• False output: only when both inputs are 0.

What is the XOR gate?

The XOR (exclusive-OR) gate gives “True” when either input, but not both, is “True”.

• Rule: it acts in the same way as the logical “either/or”.
• True output: when the two inputs are different.
• False output: when both inputs are 0, and also when both inputs are 1.
• Boolean equation: A⊕B = (A·B’) + (A’·B).

What is the NOT gate (inverter)?

The NOT gate, also called an inverter, has one input and reverses its logic state.

• Input 0: the output is 1.
• Input 1: the output is 0.

What is the NAND gate?

The NAND gate is an AND gate followed by a NOT gate, so it gives “False” only when both inputs are “True”.

• Made from: AND gate + NOT gate.
• False output: when both inputs are 1.
• True output: in every other case.

What is the NOR gate?

The NOR gate is an OR gate followed by a NOT gate, so it gives “True” only when both inputs are “False”.

• Made from: OR gate + NOT gate.
• True output: when both inputs are 0.
• False output: in every other case.

What is the XNOR gate?

The XNOR gate is an XOR gate followed by a NOT gate, so it gives “True” when both inputs are the same.

• Made from: XOR gate + NOT gate.
• True output: when both inputs are 0 or both inputs are 1.
• False output: when the inputs are different.

How do the seven logic gates compare?

The table below shows when the output of each gate is “True”.

How are logic gates combined?

Logic gates are combined by joining the output of one gate to the input of another, so that complex operations can be performed.

• Example: NAND, NOR and XNOR are each made by adding a NOT gate after AND, OR and XOR.
• In theory: there is no limit to the number of gates that can be arranged together in one device.
• In practice: only a limited number of gates can be packed into a given physical space.
• Digital ICs: arrays of logic gates are found in digital integrated circuits.
• Result: digital devices can perform more complicated operations at increasing speeds.

What are the uses of standard logic circuits?

Standard logic circuits are used to build digital electronic devices and to teach how circuits work.

1. Hardware building blocks: logic gates are the building blocks of electronic hardware components.
2. Teaching: logic gates are used in teaching about circuits.
3. AND gate: it is used to combine signals, so that an output is produced only when all inputs are high.
4. NOT gate: it is used in building a switch.

Evaluation

1. State the uses of standard logic circuits.
2. What is a logic gate?
3. List the seven basic logic gates.
4. When is the output of an AND gate “True”?
5. What is the output of an XOR gate when both inputs are 1?

Assignment

Describe the NAND, NOR and XNOR gates. For each one, state the gates it is made from and when its output is “True”.