Expressing Boolean Algebra Equation for Given Logic Circuit Diagram

how to express Boolean Algebra for this circuit ?

First look at this to remind yourself of what the logic gate symbols are

http://www.ee.surrey.ac.uk/Projects/CAL/digital-logic/gatesfunc/#example
Then start at the left side and follow the lines. Write the result of the logic gate on the line after it

So starting with A, the first gate you run into is a NOT (inverter) so you would write
/A on the line after it.  Similarly for C you have /C after the NOT. Then follow the /A line to the next gate which is AND so you have /A*B that you write on the line after that. the other AND gate should be A*/C. Then you go on to the last gate which is OR. this should give you /A*B + A*/C

I agree with Elizabeth, except I use different symbols to represent the gates -- I use '&' for AND, '|' for OR, and '!' for NOT.
If we call the output from the upper AND gate w1, then we can say w1 = (!A & B)  -- that is:  w1 = NOT(A) ANDed with B.
If we call the output from the lower AND gate w2, then we can say w2 = (A & !C) -- that is: w2 = A ANDed with NOT(C)
So Q = w1 | w2    -- that is, Q = w1 ORed with W2
So Q = (!A & B) | (A & !C)

Hi there -- I just posted a column that discusses this in a lot more detail: Logic Gates, Truth Tables, and Karnaugh Maps, Oh My!Please take a look and see if this helps -- Max