Counting on Fingers

Introduction

• Most people have 10 fingers (8 fingers + 2 thumbs)
• Commonly, we count to ten using our fingers, corresponding to the ten digits in our numbering system.

Counting Beyond Ten

• Counting to Twelve:

  • Each finger is divided into three sections (using the thumb as a pointer).
  • One hand can count up to 12 using finger sections.
  • Using both hands can count up to 60 (5 groups of 12).

• Counting to 144:

  • Each finger can represent 24 sections (3 sections x 2 hands).
  • Can now count up to 576 using both hands to mark groups of 24.

Limits of Finger Counting

• Reached a limit of countable parts on fingers.

Positional Notation

• One of the greatest mathematical inventions.
• Placement of symbols allows different magnitudes of value (e.g., the number 999).

Using Positional Value on Fingers

• Binary System:
  • Instead of sections, each finger can indicate two states (up or down).
  • Represents powers of two (1, 2, 4, 8, ... up to 512).
  • Example: Number 7 as 4+2+1 (3 fingers raised).
  • Example: Number 250 as 128+64+32+16+8+2.
  • Maximum with 10 fingers raised = 1,023.

Higher Counts with More Finger States

• If each finger can be bent halfway, there are 3 states (down, half-bent, raised).
  • Base-three positional system can count up to 59,048.
  • More finger states allow for even higher counts.

Conclusion

• Even using basic binary (2 states), we can efficiently count past 1,000.
• Computers work on a similar binary principle with switches (on or off) to perform billions of operations.