◌ 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.
Brackets beside a numeral show its components: [flag + body]. The complete numeral remains outside the brackets. Paired arrows show where value moves during promotion or demotion.
7. Subtraction
Method: Operate on flags and bodies independently. Apply Flag Demotion or Place Demotion when needed. (Use §4 to confirm the first number is the larger one.)
Clean case: 13 − 7
| 13 = 10F 3B | [+] |
| 7 = 5F 2B | [+] |
| ─────────── | |
| Flags: 10F − 5F = 5F | − = |
| Bodies: 3B − 2B = 1B | − = |
| Result: 5F 1B = 6 ✓ | [ + ] → |
With Flag Demotion: 13 − 9
Flag → Body →
| 13 = 10F 3B | [+] |
| 9 = 5F 4B | [+] |
| ─────────── | |
| Bodies: 3B − 4B → impossible → Flag Demotion | − → demote a flag first |
| 10F demotes to 5F, body gains 5: now 5F 8B | + = + |
| Flags: 5F − 5F = 0F | − = |
| Bodies: 8B − 4B = 4B | − = |
| Result: 0F 4B = 4 ✓ | [ + ] → |
With Place Demotion: [2, 0] − [1, 10]
| 0F2B, 0F0B − 0F1B, 10F0B (40 − 30) | − |
| Units: 0F0B − 10F0B → impossible → Place Demotion | − → borrow from the twenties |
| Take 1 from the twenties (2B → 1B); units receives 15F0B + 5F0B | → Units receive: + |
| 15F + 5F − 10F = 10F → units: 10F 0B | + − = [ + ◌] → |
| Twenties: 1B − 1B = 0B | − = ◌ |
| Result: 10F 0B = 10 ✓ | [ + ◌] → |