For sending input $$I_6$$​ on the output line of an 8 × 1 multiplexer, which of the following will represent the combination of selection lines?

Correct option is C

An 8 × 1 multiplexer has 8 input lines:
​$$I_0,I_1,\ldots,I_7$$​​
Since:
​$$8=2^3$$​​
it requires 3 selection lines:
​$$S_2,S_1,S_0$$​​
The selection lines represent the binary number corresponding to the selected input.
Step 1: Identify the required input
We need to send $$I_6$$​ to the output. Therefore, the selection lines must represent decimal 6.
Step 2: Convert 6 to binary
6 = 4 + 2
Hence, $$6_{10}=110_2$$​​
Therefore, $$S_2S_1S_0=110$$​​
So, $$\boxed{I_6 \rightarrow S_2S_1S_0=110}$$​​
Verification

Information Booster
1. An $$8\times1$$​ MUX requires:
​$$\log_2 8=3$$​​
selection lines.
2. The selection lines are $$S_2,S_1,S_0.$$​​
3. To select $$I_n$$​, use the 3-bit binary representation of n.
Thus,
​$$I_6\Rightarrow 6_{10}=110_2$$​​