A hexadecimal to octal tool should validate every source digit in its declared base, check the supported integer range, and only then format the value in the destination base. The original inspector described here supports bases 8, 10, and 16 for unsigned integers.
Its worked example is 2A hexadecimal = 42 decimal = 52 octal. It is a number-representation worksheet and local-tool specification, not a CSS color converter, byte encoding tool, or signed bit-pattern interpreter.
Follow the place values in both bases
Hexadecimal uses digits 0–9 and A–F, with A representing ten. For 2A, the left digit is in the sixteens place:
2 × 16 + 10 = 42.
Octal uses digits 0–7. Divide 42 by 8: the quotient is 5 and the remainder is 2, giving 52 in base 8. Check it back:
5 × 8 + 2 = 42.
| Representation | Declared base | Decimal-value check |
|---|---|---|
| 2A | 16 | 2 × 16 + 10 = 42 |
| 42 | 10 | 4 × 10 + 2 = 42 |
| 52 | 8 | 5 × 8 + 2 = 42 |
The written digits change; the integer value does not. MDN documents formatting a numeric value in a selected radix and the use of letter digits in hexadecimal. MDN, Number.toString().
Keep the original token, source base, decimal value, destination base, and formatted output in separate fields. “52” without a base label can be mistaken for decimal fifty-two.
Use a strict input policy
This proposed small tool accepts bare digits only, after trimming outer whitespace. Leading zeros are allowed. Hexadecimal letters may be upper- or lowercase; output hexadecimal uses uppercase by the example's formatting policy.
| Source base | Allowed digits | Original example |
|---|---|---|
| Octal, 8 | 0–7 | 52 accepted; 89 rejected |
| Decimal, 10 | 0–9 | 42 accepted; 2A rejected |
| Hexadecimal, 16 | 0–9, A–F, a–f | 2A or 2a accepted; 2AG rejected |
Exclude signs, prefixes such as 0x, fractional points, separators, and exponent notation from this tool's input format. These are chosen boundaries for an unsigned integer inspector, not a claim that other representations are invalid mathematics.
Validation follows the selected base. A letter E is a valid hexadecimal digit, so a hexadecimal token containing it is not automatically a decimal exponent expression. Conversely, decimal input containing E fails the decimal alphabet check. Do not infer the base from a token when the user already selected it.
If the user selects octal and enters 89, neither digit belongs to that alphabet. Show a source-base error, not a decimal interpretation or partial result.
Do not let prefix parsing stand in for validation
MDN explains that JavaScript's parseInt stops at an invalid digit and returns the valid prefix already parsed. That behavior is useful in some contexts, but it does not validate a whole input string. MDN, parseInt().
For this tool, 2AG must fail the full hexadecimal check before numeric conversion. A returned number for 2A does not make the G acceptable. Blank input and a fraction such as 2.5 also fail, while the explicit token 0 is valid and formats as 0 in every supported base.
Clear previous results on input or base changes. After converting 2A to 52, appending G must remove 52 and its place-value explanation. Leaving the old answer beside an error would hide which token it actually represented.
Keep the numeric range explicit
This original design uses JavaScript Number safe integers from 0 through 9007199254740991. MDN identifies that upper boundary as Number.MAX_SAFE_INTEGER. MDN, MAX_SAFE_INTEGER.
Validate the digit string and range before relying on the numeric value. When accumulating digits, check that the next multiply-and-add will stay within the limit. Do not let an oversized token first become an imprecise Number and then present its formatted result as exact.
A too-large input should say it is outside this tool's exact supported range. It may be a valid integer requiring a different implementation. This packet does not promise an arbitrary-size converter or silently switch its precision policy.
Within the supported range, keep the place-value trace and canonical output. Leading zeros can disappear from the formatted representation without changing the value: a source token 002A can produce octal 52. Preserve 002A in the source field so the formatting change is traceable.
Copy this prompt for the complete base inspector
Create an original self-contained offline HTML unsigned-integer
base inspector in US English, with all necessary local code in one
file. Source/destination choices: octal 8, decimal 10, hexadecimal 16.
No network calls, storage, accounts, encoding or CSS-color functions.
Input policy: trim outer whitespace, then require a nonempty whole
token. Bare digits only; source 8 permits 0-7, source 10 permits 0-9,
source 16 permits 0-9/A-F/a-f. Allow leading zeros. Reject prefixes,
signs, fractional points, separators and exponent syntax; interpret
letters strictly by declared base, so E is valid in hexadecimal.
Never accept partial 2AG or reinterpret octal 89 as decimal.
Validate every digit before conversion. Support Number safe integers
0..9007199254740991 only. Use guarded digit accumulation, checking
next multiply/add against the bound before arithmetic; do not first
round an oversized input into a Number. Too-large input gives an
explicit out-of-scope error, no arbitrary-precision promise.
Show original token, source base, exact numeric value, destination
base, canonical output and place-value derivation. Uppercase hex
output; canonical output may drop leading zeros while retaining source.
Original checks: hex 2A = 2*16+10 = 42 decimal = 52 octal;
52 octal = 5*8+2 = 42; decimal 42 -> hex 2A; hex 2a -> octal 52;
hex 002A -> octal 52 preserving source 002A; zero -> zero.
Reject hex 2AG, octal 89, blank, fractional 2.5 and oversized values.
Clear stale result/trace on input/base changes or errors. Include
actual local Convert/Reset controls, clear labels, keyboard access,
visible focus/state and readable narrow layout. Optional Copy must
copy the full base-labeled record and show actual success/failure.
No dummy controls. Not two's-complement, signed bytes, float bits,
CSS channels or a physical unit conversion. Return complete file
and manual digit/range/zero/stale-output checks. Do not claim tests
ran unless executed.
Check the generated tool by converting 2A and then appending G. The error state should show that the whole token failed and leave no result from the earlier valid prefix.
Review the value and its representations in NOS
NOS can save and render prepared HTML. A calculation companion can show the original token, declared base, place-value sum, and formatted octal result together. That makes the conversion easier to audit than an unlabeled output alone.
Keep the source token and worked record available, and verify any generated local validation against the examples. Explore NOS.