ITPEC IP October 2021 Question 3
As shown in Figure 1, there is a box that generates a single output for two inputs. The input in this box is either “Agree” or “Disagree,” and the output of “Agree” is generated only when both inputs are “Agree,” while in other cases the output of “Disagree” is generated. When three inputs are entered into two boxes as shown in Figure 2, which of the following is the correct description concerning the output?
Figure 1
Figure 2
Explanation
Agree only when all three inputs are Agree — each box is a logical AND, and two ANDs in a chain are an AND of all three inputs.
Write Agree as 1 and Disagree as 0. A box outputs 1 only when both inputs are 1, so it is AND. In Figure 2, the first box gives Input 1 AND Input 2, and the second box combines that with Input 3:
(Input 1 AND Input 2) AND Input 3
The result is 1 only if the first box outputs 1 (Inputs 1 and 2 both Agree) and Input 3 is also Agree. A single Disagree anywhere makes the output Disagree.
Answer (d)
Why not others:
- •(a) — describes OR; with one Agree and two Disagree inputs, at least one box receives a Disagree and outputs Disagree
- •(b) — describes a majority vote; Agree, Agree, Disagree still ends in Disagree
- •(c) — Disagree needs only one Disagree input, not two or more
Key rule: Chaining two-input AND gates builds a many-input AND: the output is true only when every input is true, and one false input makes it false.
Basic Theory · AI-written, may contain errors
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