{"id":56,"date":"2026-10-10T16:40:00","date_gmt":"2026-10-10T16:40:00","guid":{"rendered":"https:\/\/letterstonumbers.com\/blog\/?p=56"},"modified":"2026-10-04T16:29:18","modified_gmt":"2026-10-04T16:29:18","slug":"z26-vs-z0-mapping-differences","status":"publish","type":"post","link":"https:\/\/letterstonumbers.com\/blog\/z26-vs-z0-mapping-differences\/","title":{"rendered":"Z=26 vs Z=0 Mapping Differences"},"content":{"rendered":"

TL;DR:<\/strong> A1Z26 uses A=1 \u2026 Z=26. Zero-based schemes use A=0 \u2026 Z=25. Mixing conventions on encode and decode garbles messages\u2014label which system every assignment uses.<\/p>\n

Two common indexing bases<\/h2>\n

Human counting favors A1Z26. Programming arrays favor A0Z25. Both valid; interchangeability is not automatic.<\/p>\n

Conversion between bases<\/h2>\n

Value in A0Z25 = value in A1Z26 minus 1. Z is 25 or 26 depending base. Encode entire message in one base only.<\/p>\n

Where zero appears<\/h2>\n

If student outputs 0 in stream, suspect A0 encoding or typo for 10 split wrong. Ask before regrading entire paper.<\/p>\n

Mod arithmetic interaction<\/h2>\n

Mod 26 on 0\u201325 range differs formula from 1\u201326 range. Write formula on board during combined cipher+mod lesson.<\/p>\n

Spreadsheet column labels<\/h2>\n

Header “pos_1based” vs “pos_0based” prevents TA grading errors during university crypto recitation.<\/p>\n

Tool default<\/h2>\n

letterstonumbers.com<\/a> follows A1Z26 (1\u201326). Shift homework in 0-based must happen in student spreadsheet layer with explicit note.<\/p>\n

Exam question clarity<\/h2>\n

Print “Use A=1 indexing” in bold on test header. One point deduction policy for wrong base less harsh than full nonsense decode.<\/p>\n

Historical texts<\/h2>\n

Vintage puzzle books rarely specify\u2014solver tries both if decode fails once.<\/p>\n

Teaching both intentionally<\/h2>\n

Week compare side-by-side encode CAT: 3 1 20 vs 2 0 19. Brain stretch for gifted track.<\/p>\n

Documentation for puzzle teams<\/h2>\n

Shared Google Doc lists convention at top of every hunt season\u2014volunteer turnover breaks continuity otherwise.<\/p>\n

Exam header convention line<\/h2>\n

Print ‘Use A=1 indexing’ bold on tests\u2014one-point deduction for wrong base less harsh than full nonsense decode.<\/p>\n

Conversion formula card<\/h2>\n

A0 value = A1 value minus 1. Z is 25 or 26 depending base\u2014never mix in one message.<\/p>\n

Spreadsheet column labeling<\/h2>\n

Headers pos_1based vs pos_0based prevent TA grading errors during university recitation.<\/p>\n

Side-by-side week compare<\/h2>\n

Encode CAT as 3 1 20 vs 2 0 19\u2014gifted track brain stretch activity.<\/p>\n

Puzzle team season doc<\/h2>\n

Shared doc lists convention at top\u2014volunteer turnover breaks continuity otherwise.<\/p>\n

<\/p>\n

DATA when the programmer table starts at zero<\/h2>\n

DATA in the 1-based map is 4 1 20 1. In a 0-based table, A is 0, so the same letters are 3 0 19 0. Both rows are internally consistent and they do not match each other. Put them on one card labeled “starts at 1” and “starts at 0.” Students who write a program that returns the second row have not failed the alphabet. They have used the other base. The failure is only a failure if the assignment said “A is 1” and the program returned 0 for A.<\/p>\n

Convert one row into the other with a single rule: subtract 1 to go from the school map to the programmer table, add 1 to come back. Apply it to D only. School D is 4. Programmer D is 3. If a student subtracts 1 from every letter except A, they are special-casing the letter they find confusing. The rule has no exception at A. A becomes 0, and 0 is legal in that table even though it is illegal in A1Z26.<\/p>\n

Side-by-side card for the word INDEX<\/h2>\n

INDEX makes the bases obvious because I and X sit far apart. School values: I 9, N 14, D 4, E 5, X 24. Zero-based: 8, 13, 3, 4, 23. Print both rows and ask which base produced 24. Only the school base has 24 for X. The zero-based row never reaches 26 at all; its maximum is 25 for Z. A row that contains 26 cannot be the zero-based table. A row that contains 0 cannot be A1Z26. Those two tests classify a clue before anyone decodes a word.<\/p>\n

Do not ask students to memorize both rows for INDEX. Ask them to classify and then convert with plus or minus one. Memorizing two spelling lists is how the bases get mixed under pressure. The arithmetic is short. The labels on the card do the remembering.<\/p>\n

Exam stem that states the base in the first line<\/h2>\n

The first line of the question should be “Use A = 1.” Not a footnote, not a spoken reminder, the first line. Then ask for DATA. The expected row is 4 1 20 1. A student who produces 3 0 19 0 has ignored the stem, and the score can say so without a debate about which base is natural. Programmers in the room are not being told their table is fake. They are being told which table this item uses.<\/p>\n

Write a second item, worth fewer points, that says “Use A = 0” and asks only for the letter A. The correct answer is 0. That item exists so the zero-based thinkers get one clean win and so the rest of the class sees that 0 can be a correct answer when the stem allows it. Without that item, 0 looks like a universal mistake and the lesson collapses into a single rule of thumb.<\/p>\n

Classify a mystery row before converting DATA<\/h2>\n

Hand the class a row on a slip with no label: 4 1 20 1. Ask for the base first. The row contains neither 0 nor 26, so it could be either base, and the honest answer is “not yet classifiable” until the stem is shown. Then reveal “Use A = 1” and decode DATA. The pause is the lesson. Students who shout DATA immediately got lucky, because the same digits in the other base are not DATA.<\/p>\n

Follow with a row that is classifiable without a stem: 3 0 19 0. The zeros forbid A1Z26. This is the zero-based encoding of DATA. Students add 1 to each value and only then read letters. The two slips, shown in that order, separate “I recognize the word” from “I know which table I am in.” Recognition without the table is how the bases get mixed on the exam.<\/p>\n","protected":false},"excerpt":{"rendered":"

Spot alternate schemes before comparing answers with friends.<\/p>\n<\/div>

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