How we learn maths 我们如何学数学

Numeral Systems: Binary, Decimal & Hexadecimal


In Singapore, mathematics syllabus for P1 (primary one) includes addition, subtraction, multiplication, and division. Students work with decimal numbers. Learning about other numeral systems than decimal, they will understand: how a numeral system work in general; why decimal is the default choice.


Scope: learning how binary (base 2), decimal (base 10) and hexadecimal (base 16) systems work starting from 0 to 26; then +5, +10, etc.

Materials: 1) A3 sized paper; 2) snap cubes: 3 colors for each student; 100 pieces per color.

Increment by 1: walking through the number increment procedure with students:

  1. add one piece to the rightmost ‘ones’ column of a number system;
  2. carry over if the total units exceed the current place value – start from the ‘ones’ column till to the right:
    • snap the all the units of the current column in a straight line and now they form one unit in the preceding column;

Add more than 1: ask students to add 5 or 10 directly:

  1. Snap the cubes to be added and fill the largest place value first – for example, to add 5, one can simply put 4 into the ‘four’ column and 1 into the ‘ones’ column in the base 2 board;
  2. Carry over if necessary from the right-most.

Learned on: Feb 14, 2019

Reference: Paul A. Calter and Michael A. Calter. “Binary, Hexadecimal, Octal, and BCD Numbers”

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