Understanding the Arithmetic Logic Unit

Sep 26, 2024

Crash Course Computer Science - Episode Summary

Introduction

  • Host: Carrie Anne
  • Topic: ALU (Arithmetic Logic Unit)
  • Previous Episode: Number Representation in Binary
  • Key Concept: Computation is the main goal of a computer.

Understanding the ALU

  • Definition:
    • The ALU is the mathematical brain of a computer, handling all computations.
  • Notable ALU: Intel 74181
    • Released in 1970; first complete ALU in a single chip.

ALU Components

1. Arithmetic Unit

  • Responsible for numerical operations (addition, subtraction, etc.).
  • Basic Operation: Adding two numbers together.
  • Operations:
    • Increment (adding one to a number)
    • Simple add operations using logic gates (AND, OR, NOT, XOR).

2. Half Adder

  • Input: 2 bits (A and B)
  • Output: Sum and Carry Bit
  • Functionality:
    • Uses XOR gate for sum
    • Uses AND gate for carry
  • Special Case:
    • 1 + 1 results in 0 with a carry (output as 1, 0 in binary).

3. Full Adder

  • Input: Three bits (A, B, and Carry)
  • Output: Sum and Carry
  • Construction:
    • Two half adders and an OR gate to manage carry bits.

Building an 8-bit Ripple Carry Adder

  • Process of adding two 8-bit numbers using multiple full adders.
  • Carry bits ripple through each adder.
  • Overflow:
    • When the sum exceeds 8 bits (e.g., in games like Pac-Man).
  • Solution:
    • Extend the circuit for larger bit numbers to reduce overflow chances.
  • Modern alternatives: Carry-look-ahead adders for speed.

Additional Arithmetic Operations

  • Basic operations supported by the arithmetic unit:
    • Addition, Subtraction, AND, OR, NOT
  • Multiplication:
    • Simple ALUs use repeated addition (slower).
    • Advanced processors have dedicated multiplication circuits.

Logic Unit

  • Performs logical operations (AND, OR, NOT) and numerical tests (e.g., checking if a number is negative).
  • Example: Circuit testing if ALU output is zero using OR gates.

ALU Overview

  • High-level abstraction of the ALU components.
  • Comparison: Intel 74181 has limitations (4-bit input) compared to our 8-bit ALU design.

ALU Inputs and Outputs

  • Inputs: 8-bit numbers (A and B) and 4-bit operation code for ALU functions.
  • Output: 8-bit result of the operation, alongside flags for status (zero flag, negative flag, overflow flag).

Conclusion

  • Upcoming Topic: Memory in computing.
  • Acknowledgments: Produced with PBS Digital Studios.
  • Episode filmed in Indianapolis, Indiana.