Coding - Decoding
🔒 Log in to trackSymbol and digit coding
🔒 Log in to trackEach letter is replaced by a fixed symbol or digit. Either a table is given, or you find the symbols by matching the letters that two coded words share. Once a letter has a symbol, it keeps it for the whole question.
What symbol coding is
Each letter gets a fixed symbol or digit. If M = #, A = @ and T = %, then MAT = #@%.
Two looks come in exams:
- A table is given. You code the word letter by letter.
- No table. You get two or three coded words. You find each symbol by matching.
Once a letter has a symbol, it keeps it for the whole question.
Coding from a table
Write the symbol under each letter, in order. Then join the symbols.
Example: R = 6, O = 8, S = 3, E = 1. So ROSE = 6831 and SORE = 3861.
The same letters in a different order give a different code. So check the order of the word, not just its letters.
Conditions come before the table
Many table questions add conditions, such as:
- If the first letter is a vowel, write the codes in reverse order.
- If the first and last letters are both consonants, swap their codes.
Check every condition first. Then code from the table. If the question says "only the first condition that applies", stop at the first match.
Watch: One option is always the plain table code. It is the answer of a student who skipped the condition.
Matching without a table
When two coded words share letters, their codes share symbols.
PEN = @ # % and NET = % # &. The common letters are E and N. The common symbols are # and %. So P, the letter left in PEN, takes @, the symbol left in its code.
If the symbols follow the letter order, you can also match by place. E is 2nd in PEN, and # is 2nd in its code.
Rule: If the symbols may be in any order, match only common letters with common symbols. If two symbols still fit a letter, its code cannot be found.
Digit tables
Digits can stand for letters by a simple build. "A = 2, B = 4, C = 6" means double the position. So CAB = 6, 2, 4 = 624.
Some letters need two digits. With this build, E = 10. So count letters, not digits.
Matrix coding
Letters sit in a 5 × 5 grid. Rows and columns are numbered 1 to 5. A letter's code is its row number, then its column number.
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 1 | A | B | C | D | E |
| 2 | F | G | H | I | K |
| 3 | L | M | N | O | P |
| 4 | Q | R | S | T | U |
| 5 | V | W | X | Y | Z |
H is in row 2, column 3, so H = 23. This grid has 25 cells, so J is left out.
Decoding works the same way backwards. The code 44 32 23 reads as T (row 4, column 4), M (row 3, column 2), H (row 2, column 3), so the word is TMH.
Some papers show two grids, so one letter has two codes. Any correct pair is accepted. Choose the option in which every pair is correct.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Direct table look-up
A table of letters and their symbols or digits is printed with the question.
Write the symbol under each letter of the word, in order.
Join the symbols.
Double-check each letter against the table.
The table fixes every letter, so nothing needs to be worked out.
In a code, P = 3, L = @, A = 7, N = #, E = 5 and T = %. What is the code for PLANT?
Show solutionHide solution
P → 3, L → @, A → 7, N → #, T → %.
Join them in the order of the word.
3@7#%
Condition before the table
Conditions like 'if the word begins with a vowel, reverse the codes' are listed with the table.
Test the conditions on the word, in order.
Note the first condition that applies.
Code from the table, then apply that condition.
The condition changes the order of the symbols, not what each letter stands for.
Codes: E = &, C = @, H = %, O = #. Condition: if the word begins with a vowel, write the codes in reverse order. What is the code for ECHO?
Show solutionHide solution
ECHO begins with the vowel E, so the condition applies.
Table codes in order: & @ % #.
Reverse them.
#%@&
Match common letters with common symbols (no table)
Two coded words are given with no table, like PEN = @ # % and NET = % # &.
Circle the letters shared by the two words.
Circle the symbols shared by their codes and pair them.
Give each leftover letter the leftover symbol of the same word.
Each letter has one symbol, so shared letters force shared symbols.
In a certain code, PEN is written as @ # % and NET is written as % # &. The symbols follow the order of the letters. How is TEN written?
Show solutionHide solution
E and N are common; # and % are common. By place, E = # and N = %.
The leftovers give P = @ and T = &.
TEN = T, E, N.
& # %
Digits stand for letters by a rule
Letters are matched to digits by a pattern, such as A = 2, B = 4, C = 6.
Find the build rule from the examples (for example, double the position).
Convert the word letter by letter.
Keep one number per letter; some numbers have two digits.
The build rule is a small step on the positions, so every letter follows it.
In a code, A = 2, B = 4, C = 6 and so on. What is the code for BEAD?
Show solutionHide solution
The rule is: code = 2 × position.
B = 4, E = 10, A = 2, D = 8.
Join them in order.
41028
Matrix coding (row, column)
A 5 × 5 grid of letters with numbered rows and columns. Each letter is coded as a two-digit pair.
Find each letter's row and column in the grid.
Write the pair as row, then column.
Join the pairs for the whole word.
The grid is just a table, and the pair is the letter's address.
Rows 1 to 5 (top to bottom) are ABCDE, FGHIK, LMNOP, QRSTU, VWXYZ. Columns are numbered 1 to 5 from the left. What is the code for HIDE?
Show solutionHide solution
H is in row 2, column 3 → 23. I is row 2, column 4 → 24.
D is row 1, column 4 → 14. E is row 1, column 5 → 15.
23, 24, 14, 15
Shortcuts that save time
When two coded words share letters, circle the shared letters and the shared symbols. They belong together. The letters left over take the symbols left over.
PEN is coded as @ # % and NET as % # & (symbols in the same order as the letters). What is the code for P?
Show solutionHide solution
Common letters E and N match common symbols # and %.
P is the only letter left in PEN. @ is the only symbol left in its code.
@
Read the conditions and test them on the word before you touch the table. The table gives the symbols; the condition only changes their order.
Mistakes to avoid
Where most students lose marks on this subtopic.
Coding straight from the table without checking the conditions.
Test every condition on the word first. Then use the table.
Matching by position when the question says the symbol order may differ.
Match only common letters with common symbols.
Applying two conditions when the question says only the first one applies.
Stop at the first condition that matches.
Reading a two-digit code like 10 as two letters.
Count letters, not digits.
Writing (column, row) in matrix coding.
Row first, then column, unless the question says otherwise.
Quick revision
Read this the night before the exam.
Table given: map letter by letter, in order.
Conditions: test them before coding; stop at the first that applies if told so.
No table: common letters ↔ common symbols; leftovers pair up.
Symbols in any order: two possible symbols means the code cannot be found.
Digit codes: count letters, not digits.
Matrix code = row number, then column number, for each letter.
Practice: 12 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 12 questions
Suggested time 8 min · wrong answers go to your mistake notebook automatically.