92. The truth table of a logic gate is:
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 0 |
Find the output for the input (1, 0).
Logic Gate Truth Table – Identify the Gate and Determine the Missing Output
Logic gates are the fundamental building blocks of digital electronics. Every digital system, including computers, calculators, smartphones, communication devices, and microprocessors, performs calculations using combinations of logic gates. These gates operate on binary inputs, where each input can have only two possible values: 0 (LOW) and 1 (HIGH).
Correct Answer
Output = 1
Understanding Logic Gates
A logic gate is an electronic circuit that performs a logical operation on one or more binary inputs to produce a single binary output. The operation performed depends on the type of logic gate being used. Common logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR.
Each logic gate has a unique truth table that specifies the output corresponding to every possible combination of inputs.
Step 1: Analyze the Given Truth Table
The given entries are:
| A | B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 0 |
The only missing input combination is
(1, 0)
To determine its output, we first identify the logic gate represented by the given truth table.
Step 2: Identify the Logic Gate
Compare the given outputs with the standard truth tables of common logic gates.
The output is:
- 1 when both inputs are 0.
- 1 when one input is 0 and the other is 1.
- 0 only when both inputs are 1.
This exactly matches the truth table of a NAND gate.
A NAND gate is the complement (NOT) of an AND gate.
Its Boolean expression is
Y = (A · B)’
This means the output is the inverse of the AND operation.
Complete Truth Table of the NAND Gate
| Input A | Input B | AND Output | NAND Output |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
From the standard NAND truth table, the missing output corresponding to the input (1, 0) is clearly
1.
Why Does a NAND Gate Produce This Output?
A NAND gate first performs the AND operation and then inverts the result.
For the input (1, 0):
AND operation:
1 × 0 = 0
After applying the NOT operation:
NOT(0) = 1
Therefore, the final output becomes
1.
Importance of the NAND Gate
The NAND gate is known as a Universal Gate because any digital logic circuit can be constructed using only NAND gates. Other gates such as AND, OR, NOT, XOR, and NOR can all be implemented using suitable combinations of NAND gates. Because of this property, NAND gates are extensively used in integrated circuits, microprocessors, memory devices, and digital computers.
Comparison with Other Logic Gates
An AND gate produces an output of 1 only when both inputs are 1. A NAND gate performs exactly the opposite operation by producing an output of 0 only when both inputs are 1. This inversion makes the NAND gate extremely useful in practical digital circuit design.
Real-Life Applications
NAND gates are widely used in digital computers, arithmetic logic units (ALUs), memory circuits, flip-flops, registers, multiplexers, microcontrollers, and programmable logic devices. Modern processors contain billions of transistors arranged to implement NAND and other logic gates, enabling them to perform complex computations at extremely high speeds.
Exam-Oriented Key Concepts
Students should remember that the NAND gate is a universal gate. Its output is HIGH for every input combination except when both inputs are HIGH. Questions involving incomplete truth tables are common in competitive examinations and can usually be solved by identifying the corresponding logic gate from the known entries.
Final Answer
The given truth table represents a NAND gate. Therefore, for the input
(1, 0)
the output is
1
Final Answer: 1
