Figure It Out: Chinese and Hindu Systems

Question 1 (Chinese System)

Why alternate between Zong (vertical) and Heng (horizontal)? To distinguish between place values.

• If we used only verticals, a number like 11 (one ten, one unit) would look like ||, which could be mistaken for 2.
• By alternating, 11 becomes - | (Horizontal 1, Vertical 1), clearly showing two different positions.

Represent 41 with only Zongs: It would be |||| |. Without spaces, it looks like ||||| (5). This creates ambiguity.

Question 2 (Base-2 Gumulgal Place Value)

If we used ‘ukasar’ (2) and ‘urapon’ (1) in a place value system (Base 2):

• Digits: 0 and 1. Gumulgal has no zero.
• If we define urapon=1 and a new zero, then:
  • $10_2$ (2) = 1 urapon, 0.
  • $11_2$ (3) = 1 urapon, 1 urapon.
• Gumulgal was additive ($2+1=3$). A positional system uses powers ($1 \times 2^1 + 1 \times 2^0 = 3$).

Question 4 (8 Fingers)

If humans had 8 fingers, we would use Base-8 (Octal).

• Digits: 0, 1, 2, 3, 4, 5, 6, 7. (No digit 8).
• Representation of 25 (base-10):
  • Base-8: $25 = 3 \times 8 + 1 \rightarrow 31_8$.
  • Base-5: $25 = 1 \times 25 + 0 \times 5 + 0 \times 1 \rightarrow 100_5$.
  • Base-2: $25 = 16 + 8 + 1 = 11001_2$.