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All 8 lessons in Number Bases

  1. 1. Bundles and Bases — Deconstructing Place Value

    Understand that a number base represents a specific bundle size; define column values as powers of the base; identify legal digits for any given base; count sequentially in non-decimal bases.

  2. 2. Every Digit Has a Weight — The Expansion Algorithm

    Convert any number from Base B to Base 10 using the expansion method; correctly align powers from right to left; evaluate B⁰ correctly as 1.

  3. 3. Repeated Division — The Reverse of Expansion

    Convert Base 10 numbers to any other base using the successive division algorithm; read remainder columns from bottom to top; verify binary conversions using the odd-number rule.

  4. 4. Below the Point — Converting Fractional Parts Between Bases

    Convert bicimals to Base 10 using negative exponents; convert Base 10 decimal fractions to other bases using successive multiplication; handle mixed numbers across the radix point.

  5. 5. Base M to Base N: The Bridge Method

    Convert numbers between two non-decimal bases using Base 10 as an intermediate step; utilize the grouping shortcut to convert directly between Base 2 and Base 8.

  6. 6. Carrying in Alien Bases — When Columns Overflow

    Perform column addition and multiplication in non-decimal bases; generalize the Base 10 "carrying" rule to any base using division with remainders.

  7. 7. Borrowing Right — When the Borrowed '1' Is Not Ten

    Perform subtraction in non-decimal bases; correctly assign the base value to borrowed digits instead of 10; update donor columns correctly.

  8. 8. Why Computers Count in Twos — Binary as a Physical System

    Connect binary mathematics to physical computer hardware; define bit, nibble, and byte; use the grouping shortcut to convert between binary and Hexadecimal (Base 16); synthesize all number base skills.

Unit code SSNP2