Electrical – Is the 2 to 1 MUX universal

digital-logicmultiplexer

Is the 2 to 1 multiplexer universal? Can it create a 7 to 1 multiplexer by multiplying its logic circuit?

Best Answer

It is not universal by itself. Here is how you can implement the AND and OR gates using it:

(I am going to use the more conventional notation - I.e. the s for the selector, d0 for the first data input and d1 for the second)

The general function of such a MUX is

f = s'.d0 + s.d1

If s=a, d0=a and d1=b you get

f = a'.a + a.b = a.b

Which is AND function.

If s=a, d0=b and d1=a you get

f = a'.b + a.a = a'.b + a = a + b

Which is the OR function.

There is no way to implement the NOT function though. But! if you can use constants in addition, then it becomes possible:

If s=a, d0=1 and d1=0 you get

f = s'.1 + s.0 = s'

Which is the NOT function.

Related Solutions

Electronic – How a 2-1 multiplexer (MUX) work

The best way to get a proper understanding is to write down the truth table completely. You have 3 inputs (A, B, S), so this will give you 2\$^3\$ = 8 combinations:

S  A  B | S' C  D | Z
--------+---------+--
0  0  0 | 1  0  0 | 0
0  0  1 | 1  0  0 | 0
0  1  0 | 1  1  0 | 1
0  1  1 | 1  1  0 | 1
1  0  0 | 0  0  0 | 0
1  0  1 | 0  0  1 | 1
1  1  0 | 0  0  0 | 0
1  1  1 | 0  0  1 | 1

It's often useful to add intermediate results to make things more clear. I added a term \$C = (A \land S')\$ and \$D = (B \land S)\$. Now it should be clear that \$Z = (C \lor D)\$.

Electronic – the minimum number of NOR gates needed to implement a 2-input multiplexer

You can build the mux with 4 NOR gates, too. It doesn't require extra inverters on the inputs and outputs, if that's what you were doing. Note that the sense of the "select" input is inverted, so you need to swap the "A" and "B" inputs to compensate.

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Related Solutions

Electronic – How a 2-1 multiplexer (MUX) work

Electronic – the minimum number of NOR gates needed to implement a 2-input multiplexer

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