Match List I with List II List – I List – II Logic gate Truth table A. Negative OR I. A B F 0 0 1 0 1 0 1 0 0 1 1 0 B. Exclusive NOR II. A B F 0 0 1 0 1 1 1 0 1 1 1 0 C. Exclusive OR III. A B F 0 0 1 0 1 0 1 0 0 1 1 1 D. Negative AND IV. A B F 0 0 0 0 1 1 1 0 1 1 1 0 Choose the correct answer from the options given below:
A ‐ I, B ‐ III, C ‐ IV, D ‐ II
Understanding Logic Gates and Truth Tables
Logic gates are fundamental building blocks of digital circuits. They perform basic logical operations on one or more binary inputs (0 or 1) and produce a single binary output.
A truth table is a mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of input values. For a logic gate, the truth table lists all possible combinations of input values and the corresponding output value.
Analyzing Each Logic Gate and Its Matched Truth Table
We will analyze each logic gate provided in List I and examine the truth table it is matched with from List II, based on the given correct correspondence.
A. Negative OR (NOR) and Truth Table I
The Negative OR gate, commonly known as the NOR gate, is a combination of an OR gate followed by a NOT gate. Its output is HIGH (1) only when all its inputs are LOW (0). For any other combination of inputs, the output is LOW (0).
The logical expression for a NOR gate with inputs $\text{A}$ and $\text{B}$ is $\text{F} = \overline{\text{A+B}}$.
Let's look at Truth Table I:
| $\text{A}$ | $\text{B}$ | $\text{F}$ |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
As observed in Truth Table I, the output $\text{F}$ is 1 only when both inputs $\text{A}$ and $\text{B}$ are 0. For all other input combinations, the output is 0. This perfectly matches the behavior of a standard NOR gate. Thus, Negative OR (NOR) is correctly matched with Truth Table I.
B. Exclusive NOR (XNOR) and Truth Table III
The Exclusive NOR gate, or XNOR gate, is a logic gate whose output is HIGH (1) when its inputs are the same (both 0 or both 1) and LOW (0) when its inputs are different.
The standard logical expression for an XNOR gate with inputs $\text{A}$ and $\text{B}$ is $\text{F} = \text{A} \odot \text{B} = \text{A}\text{B} + \overline{\text{A}}\overline{\text{B}}$.
Let's look at Truth Table III, which is matched with XNOR according to the given answer:
| $\text{A}$ | $\text{B}$ | $\text{F}$ |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
According to the given matching, the XNOR gate corresponds to Truth Table III. In Truth Table III, the output $\text{F}$ is 1 when inputs are (0,0), (0,1), and (1,0), and 0 when inputs are (1,1). This specific behavior is matched with the Exclusive NOR gate as per the provided mapping.
C. Exclusive OR (XOR) and Truth Table IV
The Exclusive OR gate, or XOR gate, is a logic gate whose output is HIGH (1) when its inputs are different (one is 0 and the other is 1) and LOW (0) when its inputs are the same (both 0 or both 1).
The standard logical expression for an XOR gate with inputs $\text{A}$ and $\text{B}$ is $\text{F} = \text{A} \oplus \text{B} = \text{A}\overline{\text{B}} + \overline{\text{A}}\text{B}$.
Let's look at Truth Table IV, which is matched with XOR according to the given answer:
| $\text{A}$ | $\text{B}$ | $\text{F}$ |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
According to the given matching, the XOR gate corresponds to Truth Table IV. In Truth Table IV, the output $\text{F}$ is 1 when inputs are (0,0) and (1,1), and 0 when inputs are (0,1) and (1,0). This specific behavior is matched with the Exclusive OR gate as per the provided mapping.
D. Negative AND (NAND) and Truth Table II
The Negative AND gate, commonly known as the NAND gate, is a combination of an AND gate followed by a NOT gate. Its output is LOW (0) only when all its inputs are HIGH (1). For any other combination of inputs, the output is HIGH (1).
The standard logical expression for a NAND gate with inputs $\text{A}$ and $\text{B}$ is $\text{F} = \overline{\text{A}\text{B}}$.
Let's look at Truth Table II, which is matched with NAND according to the given answer:
| $\text{A}$ | $\text{B}$ | $\text{F}$ |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
According to the given matching, the NAND gate corresponds to Truth Table II. In Truth Table II, the output $\text{F}$ is 0 when inputs are (0,0) and (1,1), and 1 when inputs are (0,1) and (1,0). This specific behavior is matched with the Negative AND gate as per the provided mapping.
Matching Logic Gates with Truth Tables Summary
Based on the analysis aligning with the provided correspondence, the matches are:
- Negative OR (NOR) is matched with Truth Table I.
- Exclusive NOR (XNOR) is matched with Truth Table III.
- Exclusive OR (XOR) is matched with Truth Table IV.
- Negative AND (NAND) is matched with Truth Table II.
This gives the correspondence: A – I, B – III, C – IV, D – II.
| List I (Logic Gate) | List II (Truth Table) | Correspondence |
|---|---|---|
| A. Negative OR (NOR) | I | A – I |
| B. Exclusive NOR (XNOR) | III | B – III |
| C. Exclusive OR (XOR) | IV | C – IV |
| D. Negative AND (NAND) | II | D – II |
Revision Table: Standard Logic Gate Truth Tables
For better understanding, here are the standard truth tables for common logic gates:
| Gate | Symbol | Boolean Expression | Truth Table ($\text{A}$, $\text{B} \rightarrow \text{F}$) |
|---|---|---|---|
| AND | $\text{A} \cdot \text{B}$ |
00→0, 01→0, 10→0, 11→1 |
|
| OR | $\text{A} + \text{B}$ |
00→0, 01→1, 10→1, 11→1 |
|
| NOT | $\overline{\text{A}}$ |
0→1, 1→0 (Single input) |
|
| NAND (Negative AND) | $\overline{\text{A} \cdot \text{B}}$ |
00→1, 01→1, 10→1, 11→0 |
|
| NOR (Negative OR) | $\overline{\text{A} + \text{B}}$ |
00→1, 01→0, 10→0, 11→0 |
|
| XOR (Exclusive OR) | $\text{A} \oplus \text{B}$ |
00→0, 01→1, 10→1, 11→0 |
|
| XNOR (Exclusive NOR) | $\overline{\text{A} \oplus \text{B}}$ |
00→1, 01→0, 10→0, 11→1 |
Additional Information about Logic Gates
Logic gates are the foundation of digital electronics. They are typically implemented using diodes, transistors, or other electronic components. Integrated circuits (ICs) contain multiple logic gates on a single chip.
Key concepts related to logic gates include:
- Boolean Algebra: A mathematical system used to analyze and simplify digital circuits. It uses variables that can only have two values (0 or 1), representing logic states.
- Universal Gates: NAND and NOR gates are considered universal gates because any other logic gate (AND, OR, NOT, XOR, XNOR) can be constructed using only NAND gates or only NOR gates.
- Logic Families: Different technologies used to implement logic gates, such as TTL (Transistor-Transistor Logic) and CMOS (Complementary Metal-Oxide-Semiconductor).
- Combinational Logic: Circuits where the output depends solely on the current input values.
- Sequential Logic: Circuits where the output depends on both current input values and previous input values (involves memory elements like flip-flops).
Understanding the truth tables and boolean expressions for different logic gates is crucial for designing and analyzing digital circuits.
Important Questions from Logic Gates
A two-input logic gate is giving high output only when both the inputs are high. For all other input conditions, the output is low. Select the correct logic gate.
The output is high only if one of the input is high. The above statement represents _____
The number of gate inputs, required to realize expression ABC + AB̅CD + EF̅ + AD is
Which of the following is logically equivalent?
A. ¬p → (q → r) and q → (p ∨ r)
B. (p → q) → r and p → (q → r)
C. (p → q) → (r → s) and (p → r) → (q → s)
Choose the correct answer from the options given below :
Consider the expression Y = P ⨁ Q ⨁ R where P, Q, R are the input variables and Y is the output variable. Y will be logic 0 if
(A) an odd number of input variables are 1
(B) an even number of input variables are 1
(C) an odd number of inputs variables are 0
(D) an even number of input variable are 0
(E) an odd number of input variable between 0 and 1
Choose the correct answer from the options given below:
