Combining Operations using Multiplexers

To select between the four operations based on the SEL code:

Use a $4-$to$-1$ multiplexer.

The multiplexer will choose the appropriate result based on SEL:

$00$: SUM $($for addition$)$

$01$: DIFF $($for subtraction$)$

$10$: Comparison result for $AB$

$11$: Comparison result for $AB$

Hierarchical Design for $4-$bit and $8-$bit ALU

First, construct a $1-$bit ALU cell that performs all four operations.

Combine four $1-$bit cells to make a $4-$bit ALU, and use two $4-$bit ALUs to create an $8-$bit ALU.

This high$-$level design provides the necessary steps for implementing the ALU with combinational logic for each operation as specified$\mathrm{.}8$