A-level Computing 2009/AQA/Computer Components, The Stored Program Concept and the Internet/Fundamental Hardware Elements of Computers/Building circuits





A common question in the exam is to be given some boolean algebra and be asked to express it as logic gates. Let's take a look at an addition and subtraction example that you should be familiar with: $$9-(7+1)$$ First we are going to deal with the inner-most brackets $$(7+1) = 8$$ Finally we combine this answer with the $$9-$$ $$= 9-(8) = 1$$ It will work exactly in the same way for boolean algebra, but instead of using numbers to store our results, we'll use logic gates:

$$C.(A+B)$$ As with any equation, we are going to deal with the inner-most brackets first$$(A+B)$$, then combine this answer with the $$C.$$

A common question in the exam is to give you a description of a system. You'll then be asked to create a boolean statement from this description, and finally build a logic gate circuit to show this system:

Using boolean algebra describe 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: Before you rush into answering a question like this, let's try and break it down into its components. The questioner will often be trying to trick you. The two occasions that the alarm will sound are: $$B+D$$ 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: $$\overline{A}+\overline{C}$$
 * A = being towed,
 * B = window broken,
 * C = engine on,
 * D = senses movement

Combining both we get (remember the brackets!): $$(B+D).(\overline{A}+\overline{C})$$

The next step is to create a diagram out of this: