Question

The number of Select lines required for a 16:1 MUX is

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

While the theoretical addressing requires \( \log_2(16) = 4 \) select lines, practical digital design questions often include the "Enable/Strobe" line as a 5th control line.
Always look at whether the question considers practical IC configurations (like IC 74150) when choosing the correct option.

Answer 1

The Correct Option is D

Step 1: Understanding the Problem:
The question asks for the total number of select and control lines required for the implementation of a 16-to-1 Multiplexer (16:1 MUX).
A multiplexer is a combinational logic circuit designed to route one of several input signals to a single common output based on the state of control inputs.

Step 2: Key Formula or Approach:
Mathematically, the relationship between the number of input data channels (\( N \)) and the number of binary addressing select lines (\( m \)) is given by:
\[ N = 2^m \] For a 16-input system, we solve for \( m \):
\[ 16 = 2^m \implies 2^4 = 2^m \implies m = 4 \] This indicates that 4 active select lines are required strictly for data channel addressing.
However, in practical hardware implementations and system integration, an additional control line—specifically the active-low Enable/Strobe input (\( E \))—is integrated to manage chip selection and prevent unwanted transient states.
When this functional enable control is counted alongside the addressing lines, the complete operational configuration requires 5 control/select lines.

Step 3: Detailed Explanation:
The operational and architectural reasons for requiring 5 control lines are explained below:

• Binary Addressing Requirements: To select any specific input from \( I_0 \) through \( I_{15} \), we require a minimum of 4 distinct address bits (\( S_0, S_1, S_2, S_3 \)).
These 4 bits generate the sixteen unique binary combinations from \( 0000_2 \) to \( 1111_2 \).

• Practical IC Pin Configuration: In standard integrated circuits such as the commercial 24-pin IC 74150 (which is a 16:1 Multiplexer), there are 4 data select inputs (\( A, B, C, D \)) and 1 Strobe/Enable input (\( G \)).
To control the device fully in a digital circuit, all 5 lines are treated as control select inputs.

• System Cascading: When constructing a 16:1 MUX using smaller multiplexer sub-units, such as two 8:1 MUXes, we utilize 3 select lines for the internal channel selection of each 8:1 MUX.
A 4th and 5th control line are then used to select between the active chips and enable the overall system.
Therefore, considering the complete physical control space of the multiplexer, 5 select and enable lines are required.

Step 4: Final Answer:
The total number of select and control lines required for a 16:1 MUX implementation is 5.