Match the terms in List - I with the options given in List - II : List - I List – II (a) Decoder (i) 1 line to 2 nlines (b) Multiplexer (ii) n lines to 2 nlines (c) De multiplexer (iii) 2 nlines to 1 line (iv) 2 nlines to 2 n−1 lines
(a) – (ii), (b) – (iii), (c) – (i)
This question asks us to match common digital logic components with their typical input and output line configurations. Let's examine each component listed.
| List - I | List - II | Description |
|---|---|---|
| (a) Decoder | (i) 1 line to $2^n$ lines | |
| (b) Multiplexer | (ii) n lines to $2^n$ lines | |
| (c) De multiplexer | (iii) $2^n$ lines to 1 line | |
| (iv) $2^n$ lines to $2^{n-1}$ lines |
Understanding Digital Logic Components: Decoder, Mux, Demux
Let's break down the function of each component to see how it relates to the number of input and output lines.
Decoder Explained
A Decoder is a combinational logic circuit that converts a binary code from n input lines into a signal on one of $2^n$ unique output lines. For example, a 2-to-4 decoder takes 2 input bits and activates one of 4 output lines. So, if it has 'n' input lines, it will have $2^n$ output lines. The relationship is n inputs to $2^n$ outputs.
- Input: n lines
- Output: $2^n$ lines
- This matches option (ii) "n lines to $2^n$ lines".
Multiplexer (Mux) Explained
A Multiplexer, or Mux, is a data selector. It selects one of several input data lines and routes it to a single output line. The selection is controlled by a set of select lines. If there are $2^n$ input data lines, you need 'n' select lines. The Mux takes $2^n$ data inputs and produces just 1 output. The primary data flow is from many inputs to one output.
- Input (Data): $2^n$ lines
- Input (Select): n lines
- Output: 1 line
- Focusing on the data lines and the single output, this matches option (iii) "$2^n$ lines to 1 line".
Demultiplexer (Demux) Explained
A Demultiplexer, or Demux, performs the opposite function of a Multiplexer. It takes a single input data line and routes it to one of several output lines. The selection of the output line is controlled by a set of select lines. If there are $2^n$ output lines, you need 'n' select lines. The Demux takes 1 data input and distributes it to one of $2^n$ outputs.
- Input (Data): 1 line
- Input (Select): n lines
- Output: $2^n$ lines
- Focusing on the single input and the data distribution to outputs, this matches option (i) "1 line to $2^n$ lines".
Matching the Logic Components
Based on our understanding:
- (a) Decoder corresponds to (ii) n lines to $2^n$ lines.
- (b) Multiplexer corresponds to (iii) $2^n$ lines to 1 line.
- (c) De multiplexer corresponds to (i) 1 line to $2^n$ lines.
Let's summarize the matching:
| List - I Component | Matched List - II Option | Description |
|---|---|---|
| (a) Decoder | (ii) | n lines to $2^n$ lines |
| (b) Multiplexer | (iii) | $2^n$ lines to 1 line |
| (c) De multiplexer | (i) | 1 line to $2^n$ lines |
Comparing this matching with the given options, we find that option (a) – (ii), (b) – (iii), (c) – (i) is the correct combination.
Revision Table: Digital Logic Gates Summary
| Component | Inputs | Outputs | Function |
|---|---|---|---|
| Decoder | n inputs (binary code) | $2^n$ outputs (one active) | Converts binary code to unique output line activation. |
| Multiplexer (Mux) | $2^n$ data inputs, n select inputs | 1 output | Selects one data input based on select lines and passes it to output. |
| Demultiplexer (Demux) | 1 data input, n select inputs | $2^n$ outputs | Routes the single data input to one specific output line based on select lines. |
Additional Information: Applications
These fundamental digital logic components are used widely in various digital systems:
- Decoders: Used in memory addressing (selecting specific memory locations), instruction decoding in CPUs, and driving display devices like 7-segment displays.
- Multiplexers: Used for data routing, implementing logic functions, parallel-to-serial conversion, and waveform generation.
- Demultiplexers: Used for data distribution, serial-to-parallel conversion, and acting as addressable switches.
Understanding the basic function and input/output structure of Decoders, Multiplexers, and Demultiplexers is crucial for digital circuit design.
Important Questions from Combinational Circuits
Carry input is present in which of the following?
The time delay in a look-ahead carry adder is independent of
The characteristics of the combinational circuits are :
A. Output at any time is function of inputs at that time
B. Contains memory elements
C. Do not have feedback paths
D. Clock is used to trigger the circuits to obtain outputs
Choose the correct answer from the options given below :
Which of the following represents the borrow in a half subtraction?
In the __________ triggering, the output responds to the changes in the input only at the positive edge of the clock pulse at the clock input.
