Logic elements of the computer: logic gates, triggers, counters, register.
Logic bases of the computer
The mathematical apparatus of algebra of logic as the main notation in the computer is binary in which figures 1 and 0, and values of logic variables too two are used, it is very convenient for the description of how hardware of the computer functions: «1» and «0».
There are two conclusions of this fact:
· The same devices of the computer can be applied to processing and storage as the numerical information presented in binary notation, and logic variables
· At a stage of designing of hardware the algebra of logic allows to simplify considerably the logic functions describing functioning of schemes of the computer, and, therefore, to reduce number of elementary logic elements from which the main knots of the computer consist.
Data and teams in memory of the computer and in registers of the processor are represented in the form of binary sequences of various structure and length.
The logic element of the computer is a part electronic logic schemes which realizes elementary logic function.
Logic elements of computers are electronic schemes And, OR, NOT, And-NOT, OR-NOT and others (called also gates), and also the trigger.
By means of these schemes it is possible to realize any logic function describing operation of devices of the computer. Usually a gate has from two to eight entrances and one or two exits, the unit are coded by higher level of tension, than a zero (or on the contrary).
Each logic element has the symbol which expresses its logic function, but doesn't point what electronic scheme is realized in it. It simplifies the record and understanding of difficult logic schemes.
The work of logic elements is described by means of validity tables. The validity table is a tabular submission of the logic scheme (operation) in which all possible combinations of values of the validity of entrance signals (operands) together with value of the validity of a target signal (result of operation) for each of these combinations are listed.
Scheme AND. The scheme Also realizes the conjunction of two or more logic values. A symbol on block diagrams of the scheme And with two entrances and its table of the validity are presented below.
Unit on the scheme exit AND will be in only case when on all entrances there will be units. When at least on one entrance there is a zero, on an exit also there will be a zero. Operation of conjunction on function charts is designated by a sign «&», being an abbreviated notation of the English word And.
The scheme OR realizes a disjunction of two or more logic values. A symbol on block diagrams of the scheme OR with two entrances and its table of the validity are presented below.
The value of a disjunction is equal to the unit if the sum of values of operands is more or equal to 1. When at least on one entrance of the scheme OR there is a unit, on its exit also there will be a unit. Communication between an exit of z of this scheme and entrances x and y is described by a ratio: z= x v y (it is read as «x or y»).
Scheme NOT. The scheme NOT (inverter) realizes denial operation. A scheme symbol NOT and its table of the validity are presented below. If there is O on an entrance of the scheme, there is 1 on an exit. When there is 1 on an entrance, there is O on an exit.
Scheme And-NOT. The scheme And – doesn't consist of an element AND and the inverter and carries out denial of result of the scheme of AND.
Conditional meaning of the scheme And-NOT and its table of the validity are presented below.
The scheme OR-NOT. The scheme OR - doesn't consist of an element OR and the inverter and carries out denial of result of the scheme OR. A symbol of the scheme OR-NOT and its table of the validity are presented below.
The trigger is the electronic scheme which is widely applied in registers of the computer to reliable storing of one category of a binary code. The trigger has two steady conditions one of which corresponds to binary unit, and another – to binary zero.
The term the trigger occurs from the English word trigger – a latch, a trigger. To designate this scheme in English the term flip-flop is more often used that in transfer means «clap». This onomatopoeic name of the electronic scheme indicates its ability almost instantly to pass («be thrown») from one electric condition into another and on the contrary.