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boolean algebra help

Here's the question I got wrong, the website doesn't provide the correct answer:

https://media.discordapp.net/attachments/692344148212187226/954159118007021598/Screenshot_26.png

Here's my full working:
https://media.discordapp.net/attachments/692344148212187226/954158176201240626/20220317_231420.jpg?width=1440&height=529

Did I get this wrong because I used the inverse of B as the input for the B AND C gate? I may have accidentally left a space without realising it but sadly the website also doesn't display what answer I entered in
For notation, let + be OR and x be AND

Whilst your final expression is correct, it is not simplified. You should use the distributive law to simplify A×Bˉ+Bˉ×C A \times \bar{B} + \bar{B} \times C and de Morgan's law on Aˉ×Cˉ \bar{A} \times \bar{C} .

From there, a tip would be to label the value you see twice to some value, say D.

You end up with Bˉ×D+Dˉ \bar{B} \times D + \bar{D} , which is equal to Bˉ+Dˉ \bar{B} + \bar{D} (and of course substitute back in D)

My boolean algebra is a bit rusty, so if I make a mistake please point it out.
(edited 1 year ago)
Original post by MouldyVinegar
For notation, let + be OR and x be AND

Whilst your final expression is correct, it is not simplified. You should use the distributive law to simplify A×Bˉ+Bˉ×C A \times \bar{B} + \bar{B} \times C and de Morgan's law on Aˉ×Cˉ \bar{A} \times \bar{C} .

From there, a tip would be to label the value you see twice to some value, say D.

You end up with Bˉ×D+Dˉ \bar{B} \times D + \bar{D} , which is equal to Bˉ+Dˉ \bar{B} + \bar{D} (and of course substitute back in D)

My boolean algebra is a bit rusty, so if I make a mistake please point it out.


Note taken and thnx for the response, here's another question I got wrong:

https://cdn.discordapp.com/attachments/692344148212187226/954178486434684978/Screenshot_28.png

After attempting it again, I got Y = A + BC'. Is this correct?


https://media.discordapp.net/attachments/692344148212187226/954179802510819408/20220318_004918.jpg?width=497&height=663
Yup

Original post by Soul Wavel3ngth

Yup, I agree with your answer.
(edited 1 year ago)

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