# Boolean algebra equations

Discussion in 'Homework Help' started by nyasha, Apr 1, 2009.

1. ### nyasha Thread Starter Active Member

Mar 23, 2009
90
1
Let variables T represent being tall,H being heavy and F being fast. Lets consider anyone who is not tall as short,not heavy as light,and not fast as slow. Write a boolean equation to represent the following :

a) You may ride a particular amusement park ride only if you are either tall and light or short and heavy.

Attempt to solution:

F=TH'+T'H

F=TT'H + HH'T=0H+0T=0 $\leftarrow$ The answers at the back of the textbook are saying l am wrong. Where did l go wrong ?

2. ### Ratch New Member

Mar 20, 2007
1,068
3
nyasha,

Unless there some trick to the problem, it appears to me that you wrote the equation correctly. That equation is an exclusive OR, and cannot be reduced further. Your attempt to solve the equation by multiplying each term by zero (TT' and HH') cannot be justified mathematically.

Ratch

3. ### nyasha Thread Starter Active Member

Mar 23, 2009
90
1

Can't l use the that property which says a*a'=0 ? Should l have stopped here : F=TT'H + HH'T

4. ### Ratch New Member

Mar 20, 2007
1,068
3
nyasha,

You can add any number of zeros to a Boolean expression like this: TH' + T'H + TT' + HH' . Or multiply a term by 1 any number of times like this: TH'(H+H')(T+T') . But you cannot just arbitrarily multiply a term by zero just to make it zero. That's a no-no.

In any case, as I said before, you cannot simplify the exclusive OR expression of TH' + T'H any more than it already is. What does the answer book say it is?

Ratch

5. ### nyasha Thread Starter Active Member

Mar 23, 2009
90
1

So for a question like this one how would l further simplify it to have a sum of products :

b) You may NOT ride an amusement park ride if you are either tall and light, or short and heavy. Use algebra to simplify the equation to sum of products

Attempt to solution:

F=(TH')'+T'H

F=(T'+H)+T'H $\leftarrow$ Which properties can l use to simplfy this equation and end up with a sum of products ?

6. ### Ratch New Member

Mar 20, 2007
1,068
3
nyasha,

(TH'+T'H)' A NXOR expression
(T'+H)(T+H') Demorgan's Theorem
T'T+T'H'+TH + HH' Multiply it out
T'H'+TH Reduce it

Ratch

Mar 23, 2009
90
1