Logic gates solving vs Simulations

Question

Can anyone help me understand why is the output when you traced and solved using Boolean Algebra is different from Simulation softwares' output? I've traced it using boolean expression and the Q output is = a'+ c' while on simulations the Q output is = b'(a'+c'). Whenever I used Simulations the output in truth table is = 11001000 and whenever I traced and solved using boolean algebra my output in truth table is 11111010

The circuit in the second picture is what I'm referring to. ABC is my variables. The logic gates are NAND Gate, OR gate, NOT Gate, XOR Gate and NOR gate.

enter image description here

enter image description here

Answer 1

I simplified ((A*C)' ^ (C + B') + B)' as follows:

((A*C)' ^ (C + B') + B)'
   |
   | expand XOR
   V
(A*C*(C + B') + (A' + C')*C'*B + B)'
   |
   |
   V
(A*C + B*C' + B)'
   |
   |
   V
(A*C + B)'
   |
   |
   V
(A' + C')*B'