pianowithsam
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Hi, Forum!
I'm currently studying A Level Computer Science (First Year). We've got mocks in January and I'm really struggling with the boolean algebra laws and De Morgan. It just goes way over my head when we look at the questions.

Anyone got any tips on what to do when approaching the questions? Any way of remembering and applying the laws? Any way to make it easier?

Thanks a lot,
Sam.
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GgbroTG
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(Original post by pianowithsam)
Hi, Forum!
I'm currently studying A Level Computer Science (First Year). We've got mocks in January and I'm really struggling with the boolean algebra laws and De Morgan. It just goes way over my head when we look at the questions.

Anyone got any tips on what to do when approaching the questions? Any way of remembering and applying the laws? Any way to make it easier?

Thanks a lot,
Sam.
I always just looked at it as a slightly dodgy version of algebra where AND is multiplication and OR is addition (the shorthand symbols support this, which is nice). With this in mind, most mathematical techniques still apply. For example, factorisation:



A\cdot B + A\cdot C = A\cdot (B + C)

\\\

{\rm or}

\\\

A\cdot B + A = A\cdot (B + 1) = A\cdot (1) = A

That second one is very useful in the longer questions. If you start with a long string of terms, start by expanding all of them, then factor them so that you end up with a 1 in the factor (it makes all other terms redundant, which is extremely useful). Of course, you can't always manipulate it so that you get a 1, but this is often the case.

Essentially, most of the Boolean identities are simply re-written forms of mathematical equalities. For De Morgan's Laws specifically, I found them easy to remember because they're sort of opposite to each other (not literally, of course).



\overline{A\cdot B} = \overline{A} + \overline{B}

\\\

\overline{A+B} = \overline{A} \cdot \overline{B}

These are the only laws you really need to remember, as the rest are either mathematically intuitive or can be proven by truth table very easily.
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