# Logic gate

1. Nov 16, 2015

### moenste

1. The problem statement, all variables and given/known data

2. The attempt at a solution
Circuit:

A B G D E F C
0 0 1 1 1 1 0
1 1 0 1 0 1 0
0 0 1 1 1 1 0
1 1 0 1 0 1 0

Is (a) right? And any ideas what could be (b)?

2. Nov 16, 2015

### Staff: Mentor

Your A and B columns should show all possible values {00, 01, 10, 11}

The output of the D NAND gate is: A' NAND B = (A' & B)' = D

and the F NAND gate is: A NAND B' = (A & B')'

3. Nov 16, 2015

### moenste

You mean I should have four columns?

A1 0101
A2 1010
B1 0101
B2 1010

Like this?

4. Nov 16, 2015

### Staff: Mentor

No, you still have an A and a B column:

Code (Text):

A   B
--  --
0   0
0   1
1   0
1   1

5. Nov 16, 2015

### moenste

But how did you derive these numbers? My original 0101 in A and B I got from the inverter table. But I don't see how to get the ones you mention.

6. Nov 16, 2015

### Staff: Mentor

Your A and B inputs can be any binary value so since you have two inputs you have a possibility of 4 input values to the circuit as shown in the table above.

7. Nov 16, 2015

### moenste

I get it now.

So:
Code (Text):
A   B   G   D   E   F   C

0   0   1   1   1   1   0
0   1   1   0   0   1   1
1   0   0   1   1   0   1
1   1   0   1   0   1   0

8. Nov 16, 2015

### Staff: Mentor

That's what I got too. The circuit diagram has a symmetry about it which is seen in the truth table.

9. Nov 16, 2015

### moenste

10. Nov 16, 2015

### Staff: Mentor

Look at the A and B inputs and then the C output doesn't that look like some gate you're familiar with?

11. Nov 16, 2015

### insightful

I would say the "final" truth table should include only A, B, and C.

12. Nov 16, 2015

### moenste

AND has 0001 at output
OR 0111
NOR 1000
NAND 1110
Inverter 10

And I have at output 0110. The input is the same for this circuit and for AND, OR, NOR and NAND.

13. Nov 16, 2015

### insightful

Last edited: Nov 16, 2015
14. Nov 16, 2015

### moenste

15. Nov 16, 2015

### baudrunner

The truth table for this problem should have three columns - two for A and B inputs, and one for the result C.

Last edited by a moderator: Nov 16, 2015