Part $1$: Draw $8-1$ multiplexer

Using Logisim or Circuitverse, create an $8-1$ multiplexer using AND, OR$,$ and NOT logic gates only. $3$ selection bits, $8$ data inputs, and $1$ output. Including the truth table is optional.

Part $2$: Apply multiplexer to Boolean function

Consider the binary numbers from $0-15.$ The Boolean function $F(a,b,c,d)$ outputs $"1"$ only when the binary number represented by $(a,b,c,d$ is divisible by $3(0$ is divisible by $3.$

Draw the truth table for $F(a,b,c,d).$

Create the logical expressions for the multiplexer functions $\{D0$dotsD$7\}$

The challenge is to group each row in $2s$ and derive the outputs for $\{D0$dotsD$7\}$ based on the relationship between output $F$ and input $D.$

For more information, refer to the introduction of this lab procedure.

Design the circuit in Logisim or Circuitverse

You may use the Multiplexer component. In Logisim, it can be found in the folders under Plexers $$ Multiplexer.

Remember to change the Select Bits value. Don't change the Data Bits value.

Implement the circuit on the breadboard using only $74151$ and $7404$ ICs.

Picture of breadboard