Can this be simplified: Logic gates?

Question

Hey, I was wondering if the following could be simplified.

http://img164.imageshack.us/img164/5149/yaqky6.png

It's probably simpler than it looks, I'm just a bit stumped currently, I was thinking maybe a carry in the circuit with just an OR gate and a AND gate.

Any help would be appreciated, 10 points if you help me solve it :)

Answer 1

Bool alg>A.B+A.C=A.(B+C)

>B,C r inputs to OR gate then 'Anded' with A

ie output=0 or all A =0 and 1 when A=1 and either B/C=1 or both B/C=1

Answer 2

yes it can. It seems  that

((a OR c) AND b) = ((a AND b) OR (b AND c))

-----

Given that there's only 3 inputs it takes little effort to write the truth tables (Except in YA which gets rid of my "nice" formatting!)

(Or (a AND b) (b AND c)) gives

a b c  |    d  e   f

--------|---------------

0  0  0 |           0                        0                    0

0  0 1 |           0                        0                    0

0  1 0  |          0                        0                    0

0  1 1  |          0                        1                   1

1  0 0  |          0                         0                   0

1  0 1  |          0                         0                   0

1  1 0  |          1                         0                   1

1  1 1  |          1                         1                   1

where

d=(a AND b)

e=(b AND c)

f= (d OR e)

------

(AND b (a OR c) )  gives

a b c  |     d     e

--------|---------------

0  0  0 |           0                    0

0  0  1 |           1                    0

0  1  0 |           0                    0

0  1  1 |           1                    1

1  0  0 |           1                    0

1  0  1 |           1                    0

1  1  0 |           1                    1

1  1  1 |           1                    1

where

  d=(a OR c)

  e=  (b AND d)

They seem to be the same

If you're implementing it in electronics you might need to be a bit careful if input B is a timing signal. All practical gates take a small amount of time to read an input/react.

Answer 3

A and (B OR C)

Answer 4

A term appears twice, so yes it can be simplified

.. swap the gates around, do the B OR C first and then AND the result with A.

Answer 5

=A(B+C).

So you can use one OR gate and one AND gate.