Flags

How to Read This Guide: Two Tracks

Every worked example in this guide runs on two parallel tracks.

The procedure track is the actual mathematics. Every step is executable in Ńdẹ́bẹ́ alone — base 20, sub-base 5, nothing else. The design test throughout is this: if an Ńdẹ́bẹ́-only society existed, one that had never heard of base 10, could its people do this step? The worked procedures use base-20 digits, component exchanges and the stated arithmetic rules.

The commentary track is the base-10 figures (like "= 252") and the 15F3B  notation running alongside. These are an intellectual guide for readers who already know base 10 — a way to verify against what they know and understand faster. The script expressions accompany these explanations; Latin variables and component labels are teaching notation.

Wherever an example includes a base-10 check, it also includes an Ńdẹ́bẹ́ check — a verification done entirely inside base 20 — so that both kinds of reader can confirm the result on their own terms.

Pages

1. The Ńdẹ́bẹ́ Number System: Overview

Ńdẹ́bẹ́ is a writing system for the Igbo language, created by Lotanna Igwe-Odunze. Its number system honours the traditional Igbo way of counting: it is base 20 with a sub-base of 5, and every numeral from 0 to 19 is a single glyph composed of two visible layers.

Because the flag and the body are visible separately, the arithmetic of the system can be seen in the glyphs themselves: addition and subtraction can exchange values between layers; multiplication and division use those components together with place value.

2. Flags and bodies in calculations

◌ 0B: no body contribution. The dotted rectangle marks a zero body contribution; the dotted square  marks a zero flag contribution. Square brackets group the parts of one numeral. These placeholders are teaching aids, not the numeral zero or characters to insert into the final answer. Bare flags show flag contributions; complete numbers keep their normal bodies.

The isolated signs below show flag components, not complete numerals.  0F means no flag; it is not the zero numeral. Full numerals keep their bodies, including the plain body of 5, 10, and 15.

Every Ńdẹ́bẹ́ numeral is expressed as Flag + Body:

• Flag — the top marker, representing a multiple of 5. There are four flag values (0F means no flag):  0F,  5F,  10F,  15F. We also speak of a flag's level: 0F is level 0, 5F is level 1, 10F is level 2, 15F is level 3.
• Body — the lower/main form, representing units 0–4: 0B ◌, 1B, 2B, 3B, 4B. In complete numerals 5, 10 and 15, the simple stroke beneath the flag is the plain body (also called the bare body), which adds no value. The dotted rectangle only makes that zero contribution explicit in a teaching breakdown.

The 20 Numerals

Key insight: Learn the body forms, the three nonzero flags (5F, 10F, 15F), and the separate zero sign. Their values and positions let you read every numeral.

The structural fact everything else rests on: a flag step is worth 5, and the largest possible body is 4. So the flag always outweighs the body. This single fact drives comparison, rounding, and the search order in division.

Explore the numeral forms in different fonts on the Numerals page.

3. Place Values — Reading and Writing Numbers

Like all positional systems, Ńdẹ́bẹ́ uses place values. Each place is worth 20 times the place to its right.

Writing 20: Since there is no single glyph for 20 in a base-20 system, 20 is written as 1 in the twenties place and 0 in the units place — just as 10 is written in base 10.

Notation used in this guide: a multi-digit number is written with its digits separated by commas, most significant first: 0F3B, 15F2B  is a 3 in the twenties place and a 17 in the units place. In commentary, the same number appears as [3, 17]₂₀ (= 77).

4. Comparing Numbers

Before subtraction and division can be taught, a reader must be able to answer: which of two numbers is bigger? Ńdẹ́bẹ́ makes this a visual skill.

The rule

1. Count the digits. The number with more digits is bigger. (Leading zeros don't count.)
2. Same number of digits: compare the leftmost digits. Look at the flags first. The higher flag wins. If the flags tie, the higher body wins.
3. If the whole digit ties, move one digit to the right and repeat.
4. If every digit ties, the numbers are equal.

Why flags are checked first

A flag step is worth 5. The largest body is 4. So any flag advantage beats any body advantage — a number with a higher flag is bigger no matter what the bodies say. This is why a reader's eye should go to the top of the glyph first.

Examples

• 15F2B  vs 10F4B  (17 vs 14): flags 15F > 10F. First is bigger — the bodies (2B < 4B) never needed checking.
• 0F1B, 15F4B  vs 0F2B, 0F0B  ([1,19] vs [2,0], i.e. 39 vs 40): leftmost digits 1 vs 2 → second is bigger, regardless of the 19.
• 0F1B, 0F0B, 0F0B  vs 15F4B, 15F4B  ([1,0,0] vs [19,19], i.e. 400 vs 399): three digits vs two → first is bigger.

5. Promotion and Demotion Rules

These four rules govern how values move between layers and between place values.

5.1 Flag Promotion

Trigger: Body reaches 5B or more
Effect: Advance to the next flag level, subtract 5 from the body
Example: 0F + 7B → promote → 5F + 2B

5.2 Flag Demotion

Trigger: Body subtraction is impossible (body being subtracted from is too small)
Effect: Drop one flag level, add 5 to the body
Example: 10F 2B  needing to subtract 4B → demote → 5F 7B [ + ] → now subtract → 5F 3B 

5.3 Place Promotion

Trigger: Flags would reach 20F (impossible)
Effect: Produce 1B in the next place up; flags reset to  0F
Example: 15 + 7 → 15F0B + 5F2B  +  → flags: 15F + 5F = 20F → Place Promote → 1B in twenties, 0F2B  in units → 22

5.4 Place Demotion

Trigger: Current place value is too small to subtract from or divide
Effect: 1B from the place above becomes 15F0B + 5F0B  +  in the place below (= 20 units)
Example: 1 in the twenties place demotes to 15F0B + 5F0B  +  in units

Promotion and Demotion are exact inverses: 1 unit above = 20 units below, governed by multiplication and division by 20.

13. Summary: The Four Operations at a Glance

Writing expressions

These root examples use inline symbols. Fractions, extended root bars, powers, and subscripts require equation formatting. Use the Math palette in Type Ńdẹ́bẹ́ for structured expressions. The fonts do not include an OpenType MATH table.