Question

Full adder can be implemented by

• A. decoders
• B. multiplexers
• C. AND & OR gates
• D. half adders

Hint:

MUX is a universal combinational circuit—can implement full adder easily.

Answer 1

The Correct Option is B

Step 1: Write down what a full adder must compute.
A full adder combines three input bits, $A$, $B$, and a carry-in $C_{in}$, and produces a sum bit and a carry-out bit, with sum defined as $S = A \oplus B \oplus C_{in}$ and carry as $C_{out} = AB + BC_{in} + AC_{in}$.
Step 2: Recall what a multiplexer fundamentally is.
A multiplexer is really just a lookup table in hardware form, its select lines pick out which of several fixed or variable data inputs gets routed to the output, so by wiring the right values (0, 1, a variable, or its complement) onto its data inputs, a multiplexer can realise any Boolean truth table you want.
Step 3: Apply that idea to the adder's truth tables.
Treating two of the adder's three input bits (say $A$ and $B$) as the multiplexer select lines and working out what value $S$ and $C_{out}$ take for each of the four select combinations tells us exactly what to feed ($C_{in}$, $\overline{C_{in}}$, 0, or 1) into each data input, so a 4:1 multiplexer configured this way reproduces the full adder's behaviour exactly.
\[ \boxed{\text{Multiplexers}} \]