Select the outputs Y of the combination of gates shown below...

Select the outputs $Y$ of the combination of gates shown below for inputs $A=1, B=0 ; A=1, B=1$ and $A=0$, $B=0$ respectively: (A) $\left(\begin{array}{lll}0 & 0 & 1\end{array}\right)$ (B) $\left(\begin{array}{lll}1 & 0 & 1\end{array}\right)$ (C) $(111)$ (D) $\left(\begin{array}{lll}1 & 0 & 0\end{array}\right)$

Select the outputs $Y$ of the combination of gates shown below for inputs $A=1, B=0 ; A=1, B=1$ and $A=0$, $B=0$ respectively:
(A) $\left(\begin{array}{lll}0 & 0 & 1\end{array}\right)$
(B) $\left(\begin{array}{lll}1 & 0 & 1\end{array}\right)$
(C) $(111)$
(D) $\left(\begin{array}{lll}1 & 0 & 0\end{array}\right)$

Key Concepts

Logic Gates

Logic gates are the fundamental building blocks of digital circuits, designed to perform basic logical functions such as AND, OR, and NOT. They process binary inputs (0s and 1s) to produce a binary output based on a specific logic rule. In the context of the question, these gates combine to produce an overall output based on given input combinations.

Boolean Algebra

Boolean algebra is a mathematical framework used to represent and simplify digital logic circuits. It deals with binary variables and logical operations, providing a systematic way of analyzing the behavior of circuits by applying rules and identities. In this problem, it underpins the determination of output values for various input conditions.

Truth Tables

A truth table is a tool used to enumerate all possible combinations of input values and their corresponding outputs in a logic circuit. It provides a clear view of how a digital system responds to different inputs, facilitating the validation of the logic design. Here, constructing a truth table helps in mapping input combinations to the correct output sequence.

Combinational Logic Circuits

Combinational logic circuits are types of digital circuits in which the output is solely determined by the current inputs, without any memory of past inputs. They are built from interconnected logic gates and are essential for implementing functions like arithmetic operations and data routing. The problem involves analyzing such a circuit by assessing its outputs for distinct input cases.

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