Checking Boolean Algebra Solutions

[dagg3r]

hey all, got stuck on some boolean algebra just wondering if you all can check my working out thanks :)
basically the ` represent bar's and in the example no. 1 the p is barred, r is barred,and the overall function is barred hope you get the gist of things thanks

1. [(p` + qr)(pq+r`)]`

my working out is, using de morgan's rule
= [(p` + qr)]` + [(pq + r`)]
= p``*(qr)` + r``*(pq)`
=p*(qr)` + r*(pq)` \\ De morgan's rule again
= P( q` + r` ) + r(P` + q`) \\ expanded out
= pq` + r`p + rp` + q`r
\\ i use the rule that r`p + rp` = `
thus = q`(R + p)

is that right hopefully i did it correctly :)

2. (z + (x*y`)) + yx + (x*(y` + z))
thats the function my working out is i expanded it out.
thus
= (z +xy`) + yx + xy` + zx
\\ then i left it as it is as use many of the boolean rules and got
xy` +Z + YX
X(Y` + y)+ z
=X + z
\\i used the karnaugh maps and got x + z to be the simpliest function as well but was wondering ifanyone can check this out for me thanks.


3. [x` + (y`*z`)][yz` + x`][y`+z`]
= [x` + z`y`][x` + yz`][y` + z`]
\\then i used the rule that P(P+Q)=P so that means taking x` as a common factor takinga look at the first 2 functions out ofthe 3
= x`(yz` + x`)
=x` \\ now we have (y` + z`) left as a function thus
= x`(y`+z`)
\\ using de morgan's rule
=(x+yz)`

is that the simpliestform and how would i draw this as a simplified switchinig circuit because i believe the whole function barred you can't draw it?

thats all hope this isn't a load of gibberish :)

 

[Evalesco]

Yes, your working out is correct. For the third equation, you have simplified it correctly and it is in the simplest form. As for drawing a simplified switching circuit, you can draw a circuit with two inputs and one output as shown below:

Input1 --| |---- Output
Input2 --|--|

 

[thepatientmental]

Hi there, it looks like you have a good understanding of Boolean algebra and have correctly applied the rules to simplify the given functions. However, in order to fully check your solutions, it would be helpful to see the original function and the steps you took to simplify it. This would allow for a more thorough evaluation and any potential mistakes could be identified. As for drawing the simplified switching circuit, it would depend on the specific function and the components available. It would be best to consult a circuit designer or use a software tool to create the circuit. Keep up the good work!