#1

I'm helping a friend with some comp sci homework, and he's doing circuits, which I've done before, so I can find what the result is, but the question asks for a bunch of stuff that I don't know how to show. Here's the web page with the homework problems: http://www.cs.wm.edu/~debbie/cs131/hw/f08/logicf08.html

First off, I'm pretty sure about this, but not entirely, so each value starts false, right? So then the result of the first circuit would be true (1), and the second would be false (0). But I don't know how to "build a complete logic table" or what the difference between b and c is in problem 2. Or is the "logic expression" the boolean algebraic equations? The rest of the problems I get, but I'm not sure how to write all the stuff for the first two.

First off, I'm pretty sure about this, but not entirely, so each value starts false, right? So then the result of the first circuit would be true (1), and the second would be false (0). But I don't know how to "build a complete logic table" or what the difference between b and c is in problem 2. Or is the "logic expression" the boolean algebraic equations? The rest of the problems I get, but I'm not sure how to write all the stuff for the first two.

#2

anyone?

#3

I think your friend needs to attent lectures more often

The output from the circuit depends on the state of the inputs, the truth table is used to map inputs to outputs.

e.g. truth table for an AND operation:

2.c can be answered once you have the truth table for the circuit, simply compare it to the truth table of AND, OR, XOR etc.

A logical expression is simply a written form of the circuit diagram.

The output from the circuit depends on the state of the inputs, the truth table is used to map inputs to outputs.

e.g. truth table for an AND operation:

```
| A | B | O |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
```

2.c can be answered once you have the truth table for the circuit, simply compare it to the truth table of AND, OR, XOR etc.

A logical expression is simply a written form of the circuit diagram.

#4

A few ways to approach logic questions like these.

You can either draw an entire truth table and map all input combinations to their outputs, as mentioned above (i think that's what they want for q2 and 4)

You could express the circuit as a boolean expression and simplify it that way (requires a knowledge of boolean algebra rules).

You could put the values into a Karnaugh Map (works best for up to 4 different inputs) and simplify it that way into a product of sums or a sum of products expression.

Or you could go to this site:

http://www-cs-students.stanford.edu/~silver//truth/

Be warned though, this isn't going to help your friend's understanding, but it'll help them finish their homework :P

You can either draw an entire truth table and map all input combinations to their outputs, as mentioned above (i think that's what they want for q2 and 4)

You could express the circuit as a boolean expression and simplify it that way (requires a knowledge of boolean algebra rules).

You could put the values into a Karnaugh Map (works best for up to 4 different inputs) and simplify it that way into a product of sums or a sum of products expression.

Or you could go to this site:

http://www-cs-students.stanford.edu/~silver//truth/

Be warned though, this isn't going to help your friend's understanding, but it'll help them finish their homework :P

#5

1)

¬(A or B) xor (A and ¬B)

A B result

0 0 1

0 1 0

1 0 1

1 1 0

2)

(¬A and B) or (A and ¬B)

A B result

0 0 0

0 1 1

1 0 1

1 1 0

¬(A or B) xor (A and ¬B)

A B result

0 0 1

0 1 0

1 0 1

1 1 0

2)

(¬A and B) or (A and ¬B)

A B result

0 0 0

0 1 1

1 0 1

1 1 0