A simple ALU that can perform four functions: bitwise AND, bitwise OR, bitwise XOR, and bitwise NOT on two operands, A and B. 

Design logic circuits for each of these operations. Use a 2-bit opcode as the select signal for a 4x1 multiplexer:

•AND à Opcode 00: Perform bitwise AND (A AND B).

•OR    à Opcode 01: Perform bitwise OR (A OR B).

•XOR  à Opcode 10: Perform bitwise XOR (A XOR B).

•NOT  à Opcode 11: Perform bitwise NOT (A NOT B).

•Using Select Inputs (ALU), the multiplexer's output gives the result of the selected operation.

•Using Select Input(NOT), the 2x1 multiplexer output the selected variable A or B to run through the NOT gate.

•This simplistic example can be expanded with more operations, larger bit-widths, and additional complexities like handling overflow or underflow, sign extension for subtraction, and so on.