These components are known as "buses" and is simply an array of the logic gates we are familar with already. So if a system is to handle 1024 different variables at any one time, it'll need components that can process 10 input values at the same time. Using binary, we can create all combinations of 1024 using 10 bits. If there are 1024 data points, then there needs to be 1024 address. The data for these variables are stored in memory, and each data has an associated address.
Why?īecause typical computer systems have to store and deal with many variables at once. So far we have been dealing with only components that handles 1 to 3 inputs, but components in a typical computer systems will have to deal with many (16, 32, 64) inputs at once. Demultiplexor has two inputs and two outputs. One of the inputs, called the "selection bit", is used to select one of the other two inputs, called the "data bits", to be the output.ĭemultiplexors work in a reversed fashion to multiplexors. Here are the common gates, their symbols and their truth table.Ī multiplexor is a three-input gate. The goal of logic design is thus to implement the boolean logic using the least components. Typically, there're the AND (\(x\cdot y\)), OR (\(x+y\)) and NOT (\(\overline\]īut in fact, this can be achieved using just two NAND gates. Boolean Expressionsīoolean expressions are arithmetic-like notations. The number of rows on a truth table is 2 n, where n is the number of inputs.Īs you might have realized, the truth table can get pretty large if the number of inputs increased. If a boolean function accepts 2 inputs, then there are 4 possible combination: 00, 01, 10 and 11. Instead, each boolean function has a specification detailing how it works this specification can be represented in different ways:Ī truth table is a table of all possible sets of inputs alongside its output.įor a NOT gate, the boolean function it represents has the following truth table: | Input | Output |įor an AND gate within puts x and y, the boolean function it represents has the following truth table: | x | y | Output |Īs each input can receive either a 1 or 0, there are 2 possible values for that input.
Logic gates, which represents boolean functions, have names like AND, OR, NAND, but it's not very informative. An entire computer system can be built using just one of those gates. There are two types of primitive logic gates - Nand and Nor gates. Elementary logic gates are constructed from primitive logic gates. There are two categories of logic gates - primitive and elementary. Combinational chips do not have memory and thus cannot maintain state. Logic gates is a type of combinational chips, because its output depends solely on its inputs, which is what a function is. To process this data to produce something meaningful, we must pass it through some boolean functions, which takes these binary data as inputs, and output the processed binary data.īoolean functions are implemented physically as logic gates. You tap the A key on your keyboard, and the letter 'A' appears on your text editor.Īll data on your computer are stored as a combinations of bits (binary digit), which can have values of either 1s and 0s this is also known as binary data. In this article, we will explore the foundations on which a computer system process data.Īll meaningful systems takes in data as inputs, and produces outputs. ☰ Menu Computer Systems 101 - Logic Gates 16 June 2015 on computer science, logic, boolean, circuits, logic gates, AND, OR, NOT, NANDĪ computer must store and process data.
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