Revisiting Multiplexer

What is the Boolean equation for a 2-1 multiplexer?
The Boolean function for a 2-1 multiplexer is

What is the circuit diagram for a 2-1 multiplexer?
The circuit diagram for a 2-1 multiplexer is:
2-1 Multiplexer.png

Using multiplexers to perform computations

What is the circuit diagram for an XOR gate implemented with a 2-1 multiplexer?
The circuit diagram for an XOR gate implemented with a 2-1 multiplexer is:
XOR2 Gate Made From A 2-1 Multiplexer.png

What is the circuit diagram of a 1's complement generator using XOR gates?
The circuit diagram of a 1's complement generator using XOR gates is:
1's Complement Generator Made From XOR Gates.png

Using multiplexers as AND, OR

What is the circuit diagram for an AND gate implemented with a 2-1 multiplexer?
The circuit diagram for an AND gate implemented with a 2-1 multiplexer is:
AND Gate Made From A 2-1 Multiplexer.png

What is the circuit diagram for an OR gate implemented with a 2-1 multiplexer?
The circuit diagram for an OR gate implemented with a 2-1 multiplexer is:
OR2 Gate Made From A 2-1 Multiplexer.png

Shannon's Expansion Theorem

What is Shannon's Expansion Theorem?
Shannon's Expansion Theorem is a Boolean formula to convert any truth table to multiplexers.

Who created Shannon's Expansion Theorem?
Shannon's Expansion Theorem was created by Claude Shannon.

What does Shannon's Expansion Theorem state about any Boolean function?
Shannon's Expansion Theorem states that any Boolean function can be written in the form .

How are the terms of Shannon's Expansion Theorem used on a 2-1 multiplexer?
The terms of Shannon's Expansion Theorem are used on a 2-1 multiplexer like so:
Shannon's Expansion Theorem On A 2-1 Multiplexer.png

How do you use Shannon's Expansion Theorem on a Boolean function?
To use Shannon's Expansion Theorem on a Boolean function:

  1. Single out a specific variable to be .
  2. Arrange the original Boolean function to be the OR of two terms.
  3. One of the terms needs to contain .
  4. The other term needs to contain .

...

Shannon's Expansion Theorem in Practice

What's an example of using Shannon's Expansion Theorem with a Karnaugh map?
An example of using Shannon's Expansion Theorem with a Karnaugh map is:

\ 00 01 11 10
0 0 0 1 0
1 0 1 1 1

What is the explanation for Carryout?

What is another equation for the carry out of a full adder?
Another equation for the carry out of a full adder is .

What is equivalent to?
is equivalent to .

Shannon's version of Carryout:

What is the circuit diagram for a full adder that uses a multiplexer for the carry out?
The circuit diagram for a full adder that uses a multiplexer for the carry out is:
Shannon's Version Of The Full Adder.png

4-1 Multiplexer

What is the circuit diagram for a 4-1 multiplexer?
The circuit diagram for a 4-1 multiplexer is:
4-1 Multiplexer.png

Multiplexer Building Blocks

What is the circuit diagram for a 4-1 multiplexer made using 2-1 multiplexers?
The circuit diagram for a 4-1 multiplexer made using 2-1 multiplexers is:
4-1 Multiplexer Made From 2-1 Multiplexers.png

What is the circuit diagram for a 16-1 multiplexer made using 4-1 multiplexers?
The circuit diagram for a 16-1 multiplexer made using 4-1 multiplexers is:
16-1 Multiplexer Made From 4-1 Multiplexers.png

Crossbar Switches

From Copilot

A crossbar switch is a type of switch that connects multiple inputs to multiple outputs in a matrix format. This allows for any input to be connected to any output.

What is the symbol for a 2x2 crossbar switch?
The symbol for a 2x2 crossbar switch is:
2x2 Crossbar Switch Symbol.png

What is the circuit diagram for a 2x2 crossbar switch?
The circuit diagram for a 2x2 crossbar switch is:
2x2 Crossbar Switch.png