# MUX Notation A vs B vs Cin vs S notation

Original video: https://www.youtube.com/watch?time_continue=76&v=AS17X2rcRKM

http://i.stack.imgur.com/cByOK.png

1. If A, B, and C_in are all select inputs, then why is C_in labeled differently? What is the distinction? See pic at very top

2. Later, in a separate problem, I get confused by this notation in another example http://i.imgur.com/CtlWbTI.png

Is S or Cout the "top decoder"? What "top decoder mean" ? Why do we still have this C notation and is Cout somehow related to Cin? Why distinguish S and Cout with different letters? Shouldn't I just have 2^n Cout outputs?

1. There's mention of "other outputs" in this pic http://i.imgur.com/CtlWbTI.png

I only see two total outputs- S and Cout. But there should be 2^n outputs I thought

1. Later in a totally different example problem in the link below that has answers but no solutions, I get more confused by the C and C bar as two inputs instead of a C_i and it looks we input S1, S0 twice in a row except the bottom time there is an A and a B associated with it. What does this notation mean? See below

http://i.imgur.com/to9WUHR.png

## 2 Answers

4) As says in the diagram, it is a 3-input, 1-output Boolean function implemented by using a 4-to-1 mux. The 3 inputs are A, B and C.

The bottom connection represents a 2-bit/2-line bus, with A connected to S1, B connected to S0.

C is connected to the "10"-selected-input directly and to the "00"-selected-input through an inverter.

The truth table of the Boolean function partially filled out:

A B C  Z  Comment
0 0 0  1  Z=00-input=C' as selected by (A,B)=(S1,S0)=(0,0)
0 0 1  0  same as above
0 1 0  1  Z=01-input=1 as selected by (A,B)=(S1,S0)=(0,1)
...


1) C-in means Carry in. C-out Means Carry out. A and B are the bits being added together. They could have been called Q and F if you want. However C-in and C-out are standard notation for a full adder.

2) Again, S stands for SOLUTION and C-out stands for carry out. S is the answer to A added to B.

3) It's literally referring to the top line that comes out of the Decoder. That top wire of the 8 that come out will be driven high by the input 000.

4) I've not the foggiest idea what that mux is doing, because the boolean function it represents isn't shown. I'm guess it's just an arbitrary example again. S1 and S0 are referring to the bit position in this case and showing that A and B inputs are NOT interchangeable.

My guess is that you don't understand what's going on with any of these circuits. That should likely be your next question.