Combinational Circuits : MCQs & PYQs with Explanation

Option C

A 1-of-32 decoder needs 5 input lines because 2⁵ = 32, which means 5 bits can represent 32 different output lines.
A 3-to-8 decoder uses 3 input lines and produces 8 output lines. To design a 1-of-32 decoder using 3-to-8 decoders, the 5 inputs are divided into two groups:

• 3 inputs are connected to all the 3-to-8 decoders to generate the 8 outputs.
• The remaining 2 inputs are used as enable signals to select which 3-to-8 decoder will work.

Since 2 input lines can select 2²=4 decoders, we need 4 separate 3-to-8 decoders. Each decoder produces 8 outputs, so together they produce, 4*8 = 32 outputs.
Therefore, four 3-to-8 decoders are required to build a 1-of-32 decoder.

Option C

For a multiplexer, the number of select inputs is decided by the relation,
Select Inputs=log₂(Number of Data Inputs)
An 8:1 multiplexer has 8 data inputs and only one output, which means we need enough select lines to uniquely choose one of the 8 inputs. Since log₂(8) = 3, three select inputs are required.

Option B

An encoder is a combinational circuit that converts one form of data into another coded form. A Decimal to Binary Coded Encoder converts decimal digits into binary code.
In a decimal number system, there are 10 possible digits from 0 to 9, so a decimal-to-binary encoder requires 10 input lines. 
To represent these decimal digits in binary form, 4 output lines are sufficient because 4 binary bits can represent up to 16 different combinations (2⁴ = 16), which easily covers decimal values from 0 to 9.

Option B

An 8-to-1 multiplexer selects one input out of 8 possible inputs. To uniquely select any one of these 8 inputs, we need enough select lines to represent all combinations. The number of select lines (n) required is determined using the formula 2ⁿ=8. Solving this gives n=3.

Option B

A Multiplexer (MUX) is a combinational circuit that selects one input from multiple input lines and transfers it to a single output line. The selection of the input line is controlled by select lines.
If a multiplexer has, N select lines, then each select line can have two possible values (0 or 1). Therefore, total possible input combinations become M=2^N.

• M is number of input lines.
• N is number of select lines.

Option A

A half-adder is a basic digital circuit used to add two single-bit binary numbers. It produces two outputs:

• Sum, the result of adding the two input bits.
• Carry, the value that is carried to the next higher bit position if both input bits are 1.

Option D

A multiplexer (MUX) selects one input line from many and sends it to the output using select lines. The number of select lines required depends on the number of input lines and follows the formula, Number of select lines=log₂(N). Where N is the number of inputs.
For an 8 × 1 multiplexer, there are 8 input lines, so: log₂(8)=3. This means 3 select lines are required to uniquely select one of the 8 inputs.

Option A

Railway stations typically use digital clocks that display time numerically. These clocks use seven-segment displays, where each digit (0–9) is formed by lighting specific segments.

The decoder accepts four BCD inputs A, B, C and D and seven outputs a, b, c, d, e, f and g to display any decimal number from 0 to 9.

To convert BCD (Binary-Coded Decimal) input into signals that light up the correct segments, a seven-segment decoder is used. This decoder determines which segments should glow to represent each digit.

Option C

A Multiplexer (MUX) is a combinational switching circuit that has multiple input lines, one output line, and a set of control or select lines. 
The function of a multiplexer is to select one input from the set of input bits and forward it to the output, depending on the binary value applied to the control lines.

Option A

The correct circuit used to display time in railway stations is the seven-segment decoder. This digital circuit takes binary or BCD (Binary Coded Decimal) input and activates specific segments of a seven-segment ((labeled a through g)) display to show digits from 0 to 9.

Seven-segment decoders are commonly used in digital clocks and display boards because they convert numerical data into a human-readable format. Therefore, for displaying time, this is the most appropriate choice.

Option D

A BCD to Seven-Segment Decoder is used to convert Binary Coded Decimal (BCD) input into signals required to display digits on a seven-segment display.
The decoder takes a 4-bit BCD number as input and activates the appropriate segments (a to g) to display decimal numbers from 0 to 9.

Option D

A Demultiplexer (DEMUX) is a combinational logic circuit that takes one input and transfers it to one of many output lines depending on the selection inputs.
It performs the reverse operation of a multiplexer. A multiplexer selects one input from many inputs and sends it to a single output, whereas a demultiplexer distributes one input to multiple outputs.
For example, in a 1-to-4 demultiplexer, one input can be sent to any one of the four output lines based on select lines.

• A Flip-Flop is a sequential circuit that stores one bit of information.

Option A

A Multiplexer (MUX) is a combinational logic circuit that selects one input from 2ⁿ input lines and forwards it to a single output line based on n select lines. It effectively channels multiple inputs into a single output line by selecting one input at a time.

Option A

Seven-segment decoder एक डिजिटल सर्किट होता है जो बाइनरी या BCD (Binary-Coded Decimal) इनपुट को इस तरह के सिग्नल में बदलता है, जिससे seven-segment display के कुछ खास हिस्से (जिन्हें a–g से नाम दिया जाता है) जलते हैं और वो किसी संख्या (0 से 9) को दिखाते हैं।

✅ इसका इस्तेमाल आमतौर पर डिजिटल घड़ियों, कैलकुलेटर और डिस्प्ले बोर्डों (जैसे रेलवे स्टेशन पर) किया जाता है।

✅ उदाहरण: इनपुट = 0011 (BCD में 3) → डिकोडर a, b, c, d, g सेगमेंट को जलाता है ताकि डिस्प्ले पर 3 दिखाई दे।

Option C

For a multiplexer, the number of select inputs is decided by the relation,
Select Inputs=log₂(Number of Data Inputs)
An 8:1 multiplexer has 8 data inputs and only one output, which means we need enough select lines to uniquely choose one of the 8 inputs. Since log₂(8) = 3, three select inputs are required.