The combination of selection lines for sending the input $$I_{14}$$​ to output in the following multiplexer is?

Correct option is D

The given multiplexer is a 64 × 1 MUX.
Since:
​$$64=2^6$$​​
it requires 6 selection lines:
​$$S_5,S_4,S_3,S_2,S_1,S_0$$​​
The selection lines represent the binary number of the input line that is connected to the output.
Step 1: Identify the required input
We need to send:
​$$I_{14}$$​​
to the output.
Therefore, the selection lines must represent the decimal number 14 in 6-bit binary.
Step 2: Convert 14 to binary
14 = 8 + 4 + 2
Therefore:
​$$14=(001110)_2$$​​
Hence:
​$$S_5S_4S_3S_2S_1S_0=001110$$​​
So,
​$$\boxed{I_{14}\rightarrow \text{Output when }S_5S_4S_3S_2S_1S_0=001110}$$​​
Information Booster
1. A $$2^n\times1$$​ multiplexer requires n selection lines.
2. A 64 × 1 MUX therefore requires:
​$$\log_2 64=6$$​​
selection lines.
3. The six selection lines $$S_5$$​ to $$S_0$$​ form a 6-bit binary number.
4. For input $$I_k,$$​ the selection value is the 6-bit binary representation of k.
5. Thus:
​$$I_{14}\Rightarrow 14_{10}=001110_2$$​​
Additional Knowledge
For quick exam calculations:
​$$I_0\rightarrow000000\\ I_1\rightarrow000001\\ I_{14}\rightarrow001110\\ I_{31}\rightarrow011111\\ I_{32}\rightarrow100000\\ I_{63}\rightarrow111111$$​​