This document provides an overview of binary and hexadecimal number systems. It discusses converting between binary, decimal, and hexadecimal numbers, as well as mathematical operations in binary. It also covers using an IPO (input, processing, output) approach to problem-solving. Finally, it discusses setting up Ruby programming language on a flash drive to prepare for an introduction to Ruby programming in the next class. The homework assignment is to complete a math review due at the start of the next class.

1. Binary & Hexadecimal Class 3 – Number Systems II

2. Introduction Positional Number Systems Decimal Binary Hexadecimal The Power of Two

3. Agenda Review from Week 2 Binary Translating between Binary & Decimal Binary Math Hexadecimal Numbers Converting between Binary & Hex Converting between Decimal & Hex IPO Approach to Problem-Solving Ruby on Flash

4. Positional Number Systems Decimal positioning (fingers and toes) 123,456

5. Positional Number Systems Binary Number System 10101110

6. Binary-Decimal Conversion Notation 10110112 (base 2 – or binary) Convert Binary to Decimal Use positional grid and add up values e.g. 11012 ? 10012? 01102? 10002? Convert Decimal to Binary Divide into largest position, then use modulus e.g. 34510? 79110? 23310 ? Practice Exercises

7. Binary Mathematical Operations Adding and Multiplying Binary Subtracting and Dividing Binary102-12=12 Practice Exercises 10011101 1000 110111101101+101+111+101x100x111x101 1001 11011000110001 ÷ 111 111111 ÷ 1001-101-111-101

8. Positional Number Systems Hexadecimal A60F

9. Hex-Binary-Decimal Conversion Notation 101101116 (base 16 – or hexadecimal) Convert Binary to Hex Nibbles & Tribbles 101111010001 = 1011 1101 0001 = BD1 Handout: Conversion Chart (also on site) Convert Decimal to Hex Divide into largest position, then use modulus Practice Exercises

10. A Functional Example

11. Quest: Problem-Solving Approaches Various Approaches Step-by-step Algorithmic Heuristic Programmatic IPO – input, processing, output Refer to handout Group Exercise: Confusion at the restaurant Debrief

12. Quest II: Ruby on a Flash Drive Ruby on Flash – downloading and unpacking http://rubyinstaller.org/downloads Unpack to root of drive Setting Path Path command? Rubyset.bat commands Testing the installation with command prompt C:ruby -v

13. Summary Binary Number System, Operations and Conversion Hexadecimal Number System and Conversion Practical use of Hexadecimal Quest 1: IPO Approach Quest II: Ruby on Flash Next Class: Intro to Ruby Programming

14. Assignment Assignment 1: Math Review I Due start of next class Hand-in