Logical elements and their classification

Logical elements are circuits that perform logical operations. Logical elements are used in digital circuits and are used to express Boolean algebra. The system of logical operations were defined by George Boole an English mathematician in 1848.

Firs logical element was used by Erenfest in 1910. It was calculator made of telephone relays…

Let’s go to now days and clarify what is logical algebra. In logical algebra there are only two values: “True” or “False” they are identified as numbers 1 – for “true” and “0” – for “false”. Because there are two digits used, so this is why digital electronics is called as it is – “Digital Electronics” – the electronics which operates with two digits.

Logical operations may be as follows:

  • Logical negation – ¬A (in different sources negation has various markings like Ä€);

  • Logical OR – C=A + B (in other literature you may find C=AUB);

  • Logical AND – C=A*B(in other literature you may find C=A∩B).

logical_truth_tables.PNG

There is whole theory of logical algebra. You may find a lot information in Wikipedia sources.

For us there is more interesting electronic part of logical functions.

Simply there are electronic devices who perform these three basic operations:

Negation – logical NOT:

logical_NOT.png

Logical OR:

logical_OR.png

Logical AND:

logical_AND.png

By combining these three functions we can get any result. All digital electronics is based on these three logical operators.

Logical elements can be classified by working mode: statical and dynamical. Statical logical elements may work in static, pulse and dynamic modes while dynamic logical elements may only work in pulse mode.

In other hand logical elements may be gates – who reacts immediately and cannot store any value. And other elements may be combined from gates – so called latches (registers, flip-flops).

Some examples of gates: Encoder, decoder, multiplexer, demultiplexer, comparator, adder;

Latches are: triggers, registers, counters – all other that have some storage memory.

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