More computer science stuff, please help. Hint: The answers must be a number. A

Question

More computer science stuff, please help.

Hint: The answers must be a number.

A multiplexer with 8 inputs requires ___ select lines.

A multiplexer with ___ inputs requires 6 select lines.

A decoder with 5 input lines will have ____ output lines.

Note: The answers to this next question must be decimal (base 10) numbers. Don't use binary or hexadecimal

A multiplexer with 64 inputs requires _____ select lines.
A multiplexer with _____ inputs requires 4 select lines.
A decoder with 16 input lines will have _____ output lines.
A decoder with _____ input lines will have 4 output lines.

How many inputs does a function have, given that its truth table has 64 input combinations?

Hint: The answer is not 64. It has to do with the difference between "inputs" and "input combinations".

Explanation / Answer

Ingeneral,

A multiplexer of 2n inputs has n select lines
A decoder with n input lines will have 2n output lines

A multiplexer with 8 inputs requires 3 select lines. // here 2n = 8, so n = 3
A multiplexer with 64 inputs requires 6 select lines. // here n = 6, so 2n = 64
A decoder with 5 input lines will have 32 output lines. // here n = 5, so 2n = 32

A multiplexer with 64 inputs requires 6 select lines. // here 2n = 64, so n = 6
A multiplexer with 16 inputs requires 4 select lines. // here n = 4, so 2n = 16
A decoder with 16 input lines will have 65536 output lines. // here n = 16, 2n = 65536
A decoder with 2 input lines will have 4 output lines. // here 2n = 4, so n = 2

A truth table with n inputs gives 2n combinations

How many inputs does a function have, given that its truth table has 64 input combinations? 6 // here 2n = 64, so n = 6

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