Logic Gates and Digital Electronics
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1 Logic Gates and Digital Electronics Logic gates Digital systems are said to be constructed by using logic gates. These gates are the AND, OR, NOT, NAND, NOR, EXOR and EXNOR gates. The basic operations are described below with the aid of truth tables. AND gate 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 i.e. A.B. Bear in mind that this dot is sometimes omitted i.e. AB OR gate The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation. NOT gate The NOT gate is an electronic circuit that produces an inverted version of the input 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. The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate. It can also be done using NOR logic gates in the same way.
2 NAND gate This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate. The outputs of all NAND gates are high if any of the inputs are low. The symbol is an AND gate with a small circle on the output. The small circle represents inversion. NOR gate This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The outputs of all NOR gates are low if any of the inputs are high. The symbol is an OR gate with a small circle on the output. The small circle represents inversio EXNOR gate The 'Exclusive-NOR' gate circuit does the opposite to the EOR gate. It will give a low output if either, but not both, of its two inputs are high. The symbol is an EXOR gate with a small circle on the output. The small circle represents inversion.
3 Logic gates representation using the Truth table A NAND gate can be used as a NOT gate using either of the following wiring configurations. Task: Draw the circuit diagrams like the ones in the example above to show how a NOR gate can be made into a NOT gate.
4 Multi Input Logic Gates Three Input AND Gate Here is an example of a three input AND gate. Notice that the truth table for the three input gate is similar to the truth table for the two input gate. It works on the same principle, this time all three inputs need to be high (1) to get a high output. Four Input AND Gate Here is an example of a four input AND gate. It also works on the same principle, all four inputs need to be high (1) to get a high output. The same principles apply to 5, 6,..., n input gates.
5 Making Multi Input Gates Multi input gates can be made by joining gates of the same type with less inputs. The diagrams below shows how a three input AND gate and and a four input AND gate can be made out of two input AND gates. Exercise See if you can work out how multiple input OR gates work by drawing truth tables for three and four input OR gates and then check with the answers.
6 What is this all about? Digital functions are used within computers but there are also more mundane everyday examples where digital logic is used. Certain conditions some positive and some negative will produce a certain output. Car alarms have a problem - they go off when they are not supposed to. Now let's have a look at the following scenario: A car alarm is set off if a window is broken or if it senses something moving inside car, and the car is not being towed, or the engine is not on. Where: A = being towed, B = window broken, C = engine on, D = senses movement The two occasions that the alarm will sound are: but there is a caveat, the alarm will sound if either of these are true AND two things are also true, namely the engine is NOT on, and the car is NOT being towed: Combining both we get (remember the brackets!):
7 Exercise: A security system allows people of two different clearance levels access to a building. Either they have low privileges and they have a card and they are not carrying a mobile. Alternatively they have a key and are allowed to carry a mobile. The inputs available are: A = carrying a card B = carrying a mobile phone C = carrying a key Write down the boolean equation to express this:
8 Create truth tables for the following gate combinations:
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