Fundamental Hardware Elements of Computers: Boolean gate combinations

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UNIT 2 - ⇑ Fundamental Hardware Elements of Computers ⇑

← Logic Gates Boolean gate combinations Building circuits →

Now you have learnt logic gates we will take a look at how they are combined inside hardware. You may well be asked in an exam to draw your own logic gates or to work out what a combination of logic gates will output. In this section we will look at the best way to describe what a set of logic gates is in boolean algebra. Let's take a look at a quick example:

CPT-logic-gate example.svg
Exercise: Logic gate combination outputs

For the following logic gate combinations work out output Q for each:

CPT-logic-gate ex1.svg

Answer :

CPT-logic-gate ex1 Answer.svg

CPT-logic-gate ex2.svg

Answer :

CPT-logic-gate ex2 - Answer.svg

CPT-logic-gate ex3.svg

Answer :

CPT-logic-gate ex3 - Answer.svg
This equation can be simplified to equal A.B, as B . B = B, we'll find out why this is the case in the simplifying boolean equations section coming up

CPT-logic-gate ex4.svg

Answer :

CPT-logic-gate ex4 - Answers.svg
This equation can be simplified to equal 0 (always false), as \overline{A+B}.A = 0, we'll find out why this is the case in the simplifying boolean equations section coming up

CPT-logic-gate ex5.svg

Answer :

CPT-logic-gate ex5 - Answers.svg