How many control lines are there in 128 1 multiplexer?
1 Answer
A multiplexer (MUX) is a combinational circuit that allows the selection of one of several input lines and passes it to a single output line based on the values of its control (or selection) lines. The number of control lines needed for an \( n \)-input multiplexer can be determined by the formula:
\[
\text{Number of control lines} = \log_2 n
\]
Where \( n \) is the number of input lines.
### For a 128-to-1 multiplexer:
Here, \( n = 128 \), meaning the multiplexer has 128 input lines. To find the number of control lines, we apply the formula:
\[
\log_2 128 = 7
\]
So, a 128-to-1 multiplexer requires **7 control lines**.
### Explanation:
The number of control lines is determined by how many distinct combinations of selections are needed to select one of the 128 inputs. Since each control line can have two possible states (0 or 1), the total number of unique combinations that can be formed with \( k \) control lines is \( 2^k \). To select one of 128 inputs, we need enough control lines to cover all combinations, so:
\[
2^7 = 128
\]
Thus, **7 control lines** are enough to uniquely select each of the 128 inputs.
\[
\text{Number of control lines} = \log_2 n
\]
Where \( n \) is the number of input lines.
### For a 128-to-1 multiplexer:
Here, \( n = 128 \), meaning the multiplexer has 128 input lines. To find the number of control lines, we apply the formula:
\[
\log_2 128 = 7
\]
So, a 128-to-1 multiplexer requires **7 control lines**.
### Explanation:
The number of control lines is determined by how many distinct combinations of selections are needed to select one of the 128 inputs. Since each control line can have two possible states (0 or 1), the total number of unique combinations that can be formed with \( k \) control lines is \( 2^k \). To select one of 128 inputs, we need enough control lines to cover all combinations, so:
\[
2^7 = 128
\]
Thus, **7 control lines** are enough to uniquely select each of the 128 inputs.