Lesson Reach Founder
Answer the following questions based on the video lesson you just watched. All answers can be found in the video — no outside knowledge is needed.
Apply what you learned about non-base 10 number systems by working through these problems. Show all reasoning, and remember to check for illegal symbols and resist base 10 muscle memory!
Ever wonder how a computer does complex math with just two digits? This lesson from Section 4.4 of OpenStax Contemporary Mathematics breaks down addition and subtraction in non-base-10 number systems — from binary (base 2) to base 6, base 12, and base 16. The core insight: the mechanics of carrying the 1 work exactly the same way no matter what base you're in; the rollover just happens sooner or later depending on how many symbols are available. In this video: • Why computers use base 2: circuitry only recognizes two states, high current and low current (0 and 1) • Building a base-6 addition table and understanding why the digit 5 is the largest legal symbol • The 'jump method' on a number board: how 5 + 1 = 10 and 5 + 2 = 11 in base 6 • How 'carrying the 1' works in any base — rollover happens when a column runs out of legal symbols • Two common errors: using an illegal symbol (like a 9 in base 7) and accidentally applying base-10 rules • The base-13 example: why 9 + 9 ≠ 18 when you haven't hit the rollover point yet • Bases above 10 require letters as digits — base 12 and base 16 use A through F as numbers #OpenStax #ContemporaryMathematics #NumberSystems #BinaryMath #BaseSystems OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
Full access included
