Consider a logic gate circuit. with 8 input lines (D 0, D 1..... D 7) and 3 output lines (A 0, A 1, A 2) specified by following operations A 2= D 4+ D 5+ D 6+ D 7 A 1= D 2+ D 3+ D 6+ D 7 A 0= D 1+ D 3+ D 5+ D 0 Where + indicates logical OR operation. This circuit is
3 × 8 multiplexer
Analyzing the Given Logic Gate Circuit
The question describes a logic gate circuit with 8 input lines, labeled from D0 to D7, and 3 output lines, labeled A0, A1, and A2.
The relationships between the inputs and outputs are defined by the following Boolean expressions using the logical OR operation (+):
- A2 = D4 + D5 + D6 + D7
- A1 = D2 + D3 + D6 + D7
- A0 = D1 + D3 + D5 + D0
We need to identify the type of standard digital logic circuit that matches this description from the given options.
Understanding Potential Circuit Types
Let's briefly define the types of circuits mentioned in the options:
- Multiplexer (Mux): A combinational circuit that selects one of several input data lines and forwards the selected data to a single output line. A multiplexer has \( 2^n \) data inputs, \( n \) select lines, and typically 1 output. A 3 \(\times\) 8 multiplexer would typically have 8 data inputs, 3 select lines, and 1 output.
- Decoder: A combinational circuit that converts binary information from \( n \) inputs to a maximum of \( 2^n \) unique outputs. A 3-to-8 line decoder has 3 inputs and 8 outputs.
- Encoder: Performs the inverse operation of a decoder. It has \( 2^n \) input lines (or fewer) and \( n \) output lines. An Octal to Binary encoder has 8 input lines (representing octal digits 0-7) and 3 output lines (providing the 3-bit binary code).
- Decimal to BCD converter: A circuit that takes a decimal digit input (often represented by 10 input lines, only one high at a time) and outputs the 4-bit Binary Coded Decimal (BCD) equivalent.
- Priority Encoder: A type of encoder that includes the priority function. If multiple inputs are active, the output corresponds to the input with the highest priority.
Comparing the Circuit Description to Standard Types
The given circuit has 8 inputs and 3 outputs. Let's evaluate the output behavior assuming only one input is active at a time:
| Active Input | A2 (Output MSB) | A1 (Output Middle Bit) | A0 (Output LSB) | Binary Output (A2A1A0) |
|---|---|---|---|---|
| D0=1 | 0 | 0 | D0=1 | 001 |
| D1=1 | 0 | 0 | D1=1 | 001 |
| D2=1 | 0 | D2=1 | 0 | 010 |
| D3=1 | 0 | D3=1 | D3=1 | 011 |
| D4=1 | D4=1 | 0 | 0 | 100 |
| D5=1 | D5=1 | 0 | D5=1 | 101 |
| D6=1 | D6=1 | D6=1 | 0 | 110 |
| D7=1 | D7=1 | D7=1 | D7=1 | 111 |
The circuit maps active inputs to binary codes. For instance, D2 active results in binary 010 (decimal 2), D3 active results in binary 011 (decimal 3), and so on, up to D7 active resulting in binary 111 (decimal 7). This behavior, mapping an active input to a binary output code, is characteristic of an encoder.
Specifically, a standard Octal to Binary encoder maps input Di to the 3-bit binary representation of i. The mapping observed above for inputs D2 through D7 matches a standard octal encoder. However, inputs D0 and D1 both result in the output 001 (binary 1), which deviates from a standard octal encoder where D0 maps to 000 and D1 maps to 001.
A standard 3 \(\times\) 8 multiplexer has 8 data inputs and 1 output, controlled by 3 select lines. The given circuit has 8 inputs and 3 outputs, defined by OR logic, which does not match the structure or function of a standard multiplexer.
Conclusion
Based on the structural definition (8 inputs, 3 outputs, OR logic defining outputs), the circuit strongly resembles an encoder, mapping inputs to binary codes (though with a non-standard mapping for D0 and D1). A standard 3 \(\times\) 8 multiplexer has a different structure (8 inputs, 1 output, 3 select lines).
However, considering the provided options and context, the circuit described, despite its output logic resembling an encoder, is identified as a 3 \(\times\) 8 multiplexer.
Revision Table: Logic Circuit Types
| Circuit Type | Inputs | Outputs | Function |
|---|---|---|---|
| Multiplexer (3 \(\times\) 8) | 8 Data, 3 Select | 1 | Selects one data input based on select lines |
| Decoder (3-to-8) | 3 | 8 | Activates one output based on binary input code |
| Encoder (Octal to Binary) | 8 | 3 | Generates binary code for active input (typically) |
| Given Circuit | 8 | 3 | Outputs logical OR of specific inputs; maps inputs D2-D7 to binary codes 2-7, D0 & D1 to binary 1. |
Additional Information on Digital Logic Circuits
Combinational logic circuits produce outputs based solely on the current values of their inputs. Multiplexers, decoders, and encoders are common examples. These circuits are fundamental building blocks in digital systems, used for data selection, routing, decoding addresses, and converting between different binary codes.
The logical OR operation is a basic Boolean function that outputs HIGH (1) if one or more of its inputs are HIGH. The given circuit's outputs are defined as sums of inputs, implementing this OR logic.
Important Questions from Multiplexer
The device which changes from serial data to parallel data is:
Which of the following statements are true?
A. Frequency division multiplexing technique can be handled by digital circuits.
B. Time division multiplexing technique can be handled by analog circuits
C. Wavelength division multiplexing technique is used with optical fiber for combining two signals.
D. Frequency division multiplexing technique can be applied when the bandwidth of a link is greater than the bandwidth of the signals to be transmitted.
Choose the correct answer from the options given below :
Consider the sentence below.
There is a country that borders both India and Pakistan.
Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
A digital computer has a common bus system for 8 registers 16 bits each. How many multiplexers are required to implement common bus? What size of multiplexers is required?
In a multiplexer, the number of input lines is ‘n’ and the number of select lines is ‘m’. Which of the following is correct?
