the Multiplexor

Disclaimer

i do not in any way own these beautifully drawn pictures;

source credits go to wikipedia, and the 8th edition of Computer Organization and Architecture by W. Stallings

pretty, aren't they? =)

Multiplexors (MUX)

-          a device that selects one of several analog or digital input signals and forwards the selected input into a single line.

-          used in digital circuits to control signal and data routing

-          e.g.  the loading of the program counter (PC)

the number of selector pins are determined using the formula log₂(n)

The value to be loaded into the

program counter may come from one of several different sources:

-     A binary counter, if the PC is to be incremented for the next instruction

-    -     The instruction register, if a branch instruction using a direct address has just been executed

-    -     The output of the ALU, if the branch instruction specifies the address using a displacement mode

the diagram above shows an implementation of a 4-1 MUX using AND, OR, and NOT gates;

the one below is a simplified version

basically, 

-     1. There are four input lines, labeled D_o, D₁, D₂, and D₃. Only one of these lines is selected to provide

           the output signal F.

-     2. S1 and S2 implement 2-bit selection codes that are required to select the output signal F.

Deriving the Boolean Equation of a Multiplexor

the table above is a simplified form of a truth table.

From the truth-table of the 4-to-1 MUX, the Boolean Equation for output F can be derived:

F = (D_oS₁’S₂’) + (D₁S₁S₂’) + (D₂S₁S₂’) + (D₃S₁S₂)

For a 2-to-1 MUX (2 inputs, 1 output, 1 selector)

F = (AS’) + (BS)

by Lua Xin Lin B031210345