ALU Design

Introduction

This tutorial covers the design of an Arithmetic and Logic Unit (ALU) for an 8-bit computer, as explained in Ben Eater's video. Understanding the ALU is crucial for grasping how computers perform arithmetic and logic operations. This guide will help you step through the design process, building on foundational concepts like binary addition and binary representation of negative numbers.

Step 1: Understand Binary Addition

Before diving into the ALU design, ensure you comprehend how binary adders function. A binary adder takes two binary numbers and produces their sum.

• Review the workings of half adders and full adders:
  • Half Adder: Adds two single bits, outputs sum and carry.
  • Full Adder: Adds three bits (two inputs and a carry-in).

Watch this video for an in-depth explanation of binary adders: Binary Adder Video.

Step 2: Learn About Negative Number Representation

Understanding how computers represent negative numbers in binary is essential for designing the ALU.

• Familiarize yourself with Two's Complement:
  • This method allows a computer to perform subtraction using addition.
  • To find the Two's Complement, invert all bits of the number and add one.

For more details, check this video: Negative Numbers in Binary.

Step 3: Design the ALU

Now that you have a solid foundation, proceed with the design of the ALU.

• Define Functions: Determine what operations your ALU will support:

  • Addition
  • Subtraction
  • Logical AND
  • Logical OR

• Create the Circuit:

  • Use logic gates (AND, OR, NOT) and adders.
  • Arrange the gates to execute the defined functions based on input control signals.

Step 4: Integrate Control Logic

Incorporate control logic to manage which operation the ALU performs at any given time.

• Control Signals:
  • Develop a system to send signals to the ALU indicating which operation to perform.
  • Use multiplexers to select the appropriate data inputs for the desired operation.

Step 5: Testing the ALU

After assembling the ALU, it's crucial to test it to ensure all operations function correctly.

• Unit Testing: Run tests for each operation:
  • Check that addition produces the correct result.
  • Verify subtraction by checking addition of the two's complement.
  • Confirm logical operations return expected outputs.

Conclusion

Designing an ALU involves understanding binary arithmetic, negative number representation, and effectively using logic gates. By following these steps, you can create a functional ALU for an 8-bit computer. For further exploration, consider implementing the ALU in a complete computer architecture or experimenting with additional operations. You can find additional resources and support Ben Eater on his Patreon or check his comprehensive guide at Eater.net.