Help Please! Cant do this Boolean Algebra problem, brain not good enough : (

Jaaames

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Hi, would really appreciate it if someone could help me with this problem:

Show with boolean algebra that:

NotA . NotB XOR NotC . NotD = (A + B) XOR (C + D)

Thanks very much in advance

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RogerOxon

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(Original post by Jaaames)
Hi, would really appreciate it if someone could help me with this problem:

Show with boolean algebra that:

NotA . NotB XOR NotC . NotD = (A + B) XOR (C + D)

Thanks very much in advance

De Morgan's gets you part of the way, then you need to use a property of XOR.

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Jaaames

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(Original post by RogerOxon)
De Morgan's gets you part of the way, then you need to use a property of XOR.

Cheers Roger,

I thought so, this is what I've got so far:

Name: Question 6 workings.png
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What do you mean by 'need to use a property of XOR'?

Thanks for your help.

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RogerOxon

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First apply De Morgan's to each side of your XOR:

$\overline{x}.\overline{y}= \overline{x+y}$

You should have something that differs from what you want by having a not on each side of the XOR. Look at the truth table for XOR to see the next step.

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Jaaames

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(Original post by RogerOxon)
First apply De Morgan's to each side of your XOR:

$\overline{x}.\overline{y}= \overline{x+y}$

You should have something that differs from what you want by having a not on each side of the XOR. Look at the truth table for XOR to see the next step.

Thanks Roger,

After a bit of head scratching I managed to do it:

Name: Question 6 workings.png
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Thanks so much for your help though

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Jaaames

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(Original post by Jaaames)
Thanks Roger,

After a bit of head scratching I managed to do it:

Thanks so much for your help though

Name: Question 6 workings 2.jpg
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RogerOxon

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(Original post by Jaaames)

Good. Here's how I would do it:

$\overline{x}.\overline{y}= \overline{x+y}$

$\therefore (\overline{A}.\overline{B}) \; XOR \; (\overline{C}.\overline{D}) = \overline{A+B} \; XOR \; \overline{C+D}$

$x \; XOR \; y=\overline{x} \; XOR \; \overline{y}$ (Easiest to show this with a Karnaugh map)

$\therefore \overline{A+B} \; XOR \; \overline{C+D} = (A+B) \; XOR \; (C+D)$

$\therefore (\overline{A}.\overline{B}) \; XOR \; (\overline{C}.\overline{D}) = (A+B) \; XOR \; (C+D)$

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