Design an Arithmetic Logic Unit (ALU) which can perform the following arithmetic and logic operations:  

1. Add

2. Subtract

3. NAND

4. NOT

5. NOR

1. Construct the diagram of a 1-bit simple ALU that performs the above arithmetic operation (addition and subtraction) and the THREE (3) logical operations.
2. Using the 1-bit ALU as a block, construct a larger ALU, which can perform all the functions of the 1-bit ALU but with nibble sized inputs. 
   
3. Implement an 8-bit ALU with an 8-bit Memory Registers to store the results so it can be used as input for future ALU operations. This must be implemented in CircuitVerse or a similar circuit simulation software to demonstrate you have a working ALU Design.