Computer Systems

#Understanding the Machine One Bit at a Time

0. #Introduction

   0. Introduction
      • Abstraction Stack
      • What is Abstraction?
      • Roadmap
      • Prerequisites
   1. Boolean Logic
      • Booleans and Binary
      • Logic
      • Operations on Binary Values
      • Check your understanding!
      • Boolean Functions
      • Truth Table to Boolean Function
      • Steps to convert Truth Table to a Boolean Function
      • Gate Implementation
   2. Simplifying logic gates
      • Factoring
      • Boolean Algebra
      • Boolean Laws Cheatsheet
      • Derived Boolean Laws Cheatsheet
      • Example Simplification
      • Practice Problem C
   3. NAND theorem
      • The NAND Gate
      • Building the NAND Gate
      • The Universal Gate
      • Hardware Simulator
      • HDL
   4. Elementary Logic Gates
      • 1.2.1 The Nand Gate
      • 1.2.2 Basic Logic Gates
      • 1.2.3 Multi-Bit Versions of Basic Gates
      • 1.2.4 Multi-Way Versions of Basic Gates
      • 1.3 Implementation

1. #Language

   0. Language
      • Bits
      • What can we do with 1 bit?
      • 2 bits
      • 3 bits
      • Finite Limit of Information
   1. Binary Numbers
      • How to convert a binary number to a decimal number?
      • How to convert a decimal number to a binary number?
   2. Negative Binary Numbers
      • Negative aka Signed Numbers in Two’s Complement
      • How Two’s complement encoding works
      • Multiple Meanings
      • Multiple interpretations of bits
   3. Binary Addition
      • How to add binary numbers?
   4. Binary Subtraction
      • How to subtract binary numbers?
      • Overflow Problems
   5. ALU

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