The output is high only if one of the input is high. The above statement represents _____
EX - OR gate
Understanding Logic Gate Behavior
The question asks us to identify a logic gate based on its output behavior: the output is high only if one of the inputs is high. This specific condition describes how the gate reacts to different combinations of input signals (usually represented as 0 for low and 1 for high).
Analyzing the Logic Gates
Let's examine the common logic gates and their truth tables to see which one matches the description:
- NAND gate: The output is low (0) only when both inputs are high (1). In all other cases (0,0; 0,1; 1,0), the output is high (1). This does not match the condition "high only if one of the input is high" because the output is also high when both inputs are low.
- OR gate: The output is high (1) if at least one input is high (1). This means if inputs are (0,1), (1,0), or (1,1), the output is high (1). The output is low (0) only when both inputs are low (0,0). This does not match the condition "high only if one of the input is high" because the output is high even when *both* inputs are high.
- AND gate: The output is high (1) only when both inputs are high (1). In all other cases (0,0; 0,1; 1,0), the output is low (0). This clearly does not match the condition "high only if one of the input is high".
- EX-OR gate (Exclusive OR gate): The output is high (1) only when the inputs are different. This means if inputs are (0,1) or (1,0), the output is high (1). If the inputs are the same, (0,0) or (1,1), the output is low (0). This perfectly matches the condition "high only if one of the input is high", as this occurs precisely when the inputs are different (one high, one low).
Truth Table Comparison
Let's look at the truth tables for these gates. Let A and B be the inputs and Y be the output.
| Input A | Input B | AND Gate (Y) | OR Gate (Y) | NAND Gate (Y) | EX-OR Gate (Y) |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 |
Comparing the truth tables with the description "output is high only if one of the input is high", we see that the EX-OR gate output is 1 exactly when one input is 0 and the other is 1. When both inputs are the same (both 0 or both 1), the output is 0.
The boolean expression for the EX-OR gate is typically written as $A \oplus B$ or $A\bar{B} + \bar{A}B$.
Conclusion
Based on the analysis of the truth tables and the behavior described, the gate whose output is high only if one of the inputs is high is the EX-OR gate.
Revision Table: Logic Gates Summary
| Gate | Description | Output for (1,1) | Output for (0,0) | Output for (0,1) or (1,0) |
|---|---|---|---|---|
| AND | Output high only if ALL inputs high | High (1) | Low (0) | Low (0) |
| OR | Output high if ANY input is high | High (1) | Low (0) | High (1) |
| NAND | Output low only if ALL inputs high (NOT of AND) | Low (0) | High (1) | High (1) |
| NOR | Output low if ANY input is high (NOT of OR) | Low (0) | High (1) | Low (0) |
| EX-OR | Output high only if inputs are DIFFERENT | Low (0) | Low (0) | High (1) |
| EX-NOR | Output high only if inputs are the SAME (NOT of EX-OR) | High (1) | High (1) | Low (0) |
Additional Information: Applications of EX-OR Gate
The EX-OR gate, often called the "exclusive OR" gate, has several practical applications in digital electronics due to its unique property:
- Equality Detector: An EX-NOR gate (the inverse of EX-OR) can act as an equality detector, outputting high when inputs are the same. Conversely, the EX-OR gate acts as an inequality detector.
- Parity Checker/Generator: EX-OR gates are fundamental components in circuits that check or generate parity bits for error detection in data transmission. A series of EX-OR gates can determine if the number of '1's in a data word is even or odd.
- Arithmetic Circuits: They are used in constructing arithmetic circuits like adders. A half adder uses an EX-OR gate for the sum output and an AND gate for the carry output.
- Data Encryption: EX-OR operations are simple and reversible ($\text{A} \oplus \text{B} \oplus \text{B} = \text{A}$), making them useful in simple data encryption methods where data is XORed with a key.
Understanding the truth table and the specific conditions for a high output is crucial for identifying logic gates.
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 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:
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:
