What does a demultiplexer do?

Sends one input to one of many outputs chosen by select lines

Selects one of many inputs and sends it to one output

Converts a code to one active line without data

How can a DEMUX act as a decoder?

Hold the data input at 1 (or use it as enable) so the selected output goes active

After adding 010 + 101 = 111 with no end carry, what is the result?

-1, because no carry means a negative result in 2's complement form

+1, because the end carry is dropped

2081 Baisakh · 2+4 marks

DEMUX applications; 010 − 011 by 2's complement

Short answer

A demux routes one data line to a selected output, enabling data distribution, serial-to-parallel conversion, and decoder operation. Subtracting 011 from 010: 2's complement of 011 is 101; adding 010+101=111 with no end carry indicates negative result; its magnitude from 2's complement is 001, so answer -1.

Explain the applications of de-multiplexer. Subtract 011 from 010 using 2's complement method.

Applications of a demultiplexer

A demultiplexer sends one input to one of many outputs selected by the select lines. Uses:

Data distribution / serial-to-parallel conversion: serial data on one line is sent to different output lines in turn.
Time-division demultiplexing in communication: separating signals from a shared line at the receiver (e.g. telephone exchanges).
Decoder function: with data input held at 1 (or used as enable), a 1: $2^n$ DEMUX works as an $n$ -to- $2^n$ decoder for memory address decoding and chip selection.
Boolean function generation: outputs give minterms, which can be ORed to realize functions (e.g. full adder).
Control signal routing in ALUs, microprocessors and multi-display systems.

(010)₂ − (011)₂ using 2's complement

Here $010 = 2$ and $011 = 3$ ; expected result $2 - 3 = -1$ .

2's complement of the subtrahend $011$ $011$ :
- 1's complement: $100$
- add 1: $100 + 1 = 101$
Add to the minuend:

     010    (+2)
   + 101    (2's complement of 3)
   -----
     111    (no end carry)

There is no end carry, so the result is negative and is in 2's complement form. Take the 2's complement of $111$ $111$ to get its magnitude:
- 1's complement: $000$
- add 1: $001$

Answer: $(010)_2 - (011)_2 = -(001)_2 = (-1)_{10}$ . In 3-bit 2's complement form the result is stored as $111$ .

✓ Answer checked by Claude Opus 5.5 (high effort)

Multiplexer tree; 1:16 DEMUX from 1:4 · Digital Logic, chapter 4
De Morgan's theorem and (-47+27) by 2's complement · Digital Logic, chapter 2
DEMUX vs decoder; 4×16 decoder from 2×4 · Digital Logic, chapter 4
Full adder using decoder; (57−43) by 2's complement · Digital Logic, chapter 4
FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement · Digital Logic, chapter 5
2's complement: (1111)2 − (1110)2 · Basic Electronics Engineering, chapter 6
2's complement: (1111)2 − (1100)2 · Basic Electronics Engineering, chapter 6
2's complement subtraction; AND using NOR · Basic Electronics Engineering, chapter 6

All Digital Logic chapter 4 questions →

DEMUX applications; 010 − 011 by 2's complement

Applications of a demultiplexer

(010)₂ − (011)₂ using 2's complement

Related questions