Digital circuit: truth table and Karnaugh map

Problem statement

Given the digital circuit in the figure:

[Figure: circuit with four inputs, $A$, $B$, $C$ and $D$. A two-input OR gate receives $B$ and $C$; a three-input OR gate receives $A$, complemented $C$ and complemented $D$; and another two-input OR gate receives complemented $C$ and complemented $B$. The outputs of the three OR gates enter a three-input AND gate, whose output is $F(A,B,C,D)$.]

a) Obtain the truth table of the function $F(A,B,C,D)$. (1 mark)

b) Obtain the most simplified logic expression of the function $F(A,B,C,D)$ as a sum of products, using the Karnaugh map method. (0.5 marks)

c) Draw the corresponding simplified circuit using NOT, AND and OR gates with the appropriate number of inputs. (0.5 marks)

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Technology and Engineering · Question 4.2. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.