Better to know some
... than all
Basic Gates and Functions
Boolean functions may be practically implemented by using electronic gates. The following points are important to understand.
1) Electronic gates require a power supply.
2) Gate INPUTS are driven by voltages having two nominal values, e.g. 0V and 5V representing logic 0 and logic 1 respectively.
3) The OUTPUT of a gate provides two nominal values of voltage only, e.g. 0V and 5V representing logic 0 and logic 1 respectively.
4) There is always a time delay between an input being applied and the output responding.
Digital systems are said to be constructed by using three basic logic gates. These gates are the AND gate, OR gate and NOT gate. There also exists other logical gates, like the NAND, and the EOR gates. We will only be looking at the first three gates. The basic operations are described below.
The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high. A dot (.) is used to show the AND operation. Bear in mind that this dot is usually omitted, as shown at the output above.
The OR gate is an electronic circuit that gives a high output if one or more of its inputs are high. A plus (+) is used to show the OR operation.
The NOT gate is an electronic circuit that produces an inverted version of the input's logic at its output. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or A with a bar over the top, as shown at the outputs above.
This is a NOT-AND circuit which is equal to an AND circuit followed by a NOT circuit. The outputs of all NAND gates are high if any of the inputs are low.
This is a NOT-OR circuit which is equal to an OR circuit followed by a NOT circuit. The outputs of all NOR gates are low if any of the inputs are high.
The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high. An encircled plus sign () is used to show the EOR operation.
The NAND and NOR are called universal functions since with either one the AND and OR functions and NOT can be generated.
A function in sum of products form can be implemented using NAND gates by replacing all AND and OR gates by NAND gates.
A function in product of sums form can be implemented using NOR gates by replacing all AND and OR gates by NOR gates.
Logic gate symbols
Table shows the input/output combinations for the NOT gate together with all possible input/output combinations for the other gate functions. Also note that a truth table with 'n' inputs has 2n rows.
A NAND gate can be used as a NOT gate using the following wiring.
Logic gates representation using the Truth table
And Truth Table
Or Truth Table
Exclusive Or Truth Table