ForHosting KIT · Developer Utilities

Count leading zeros calculator

Count the zero bits above the highest one-bit of a number in a fixed-width word: 16 in 8 bits is 00010000, so the count is 3. You also get the bit length and the padded binary. Free in your browser.

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Worked example

If you enter
Value
16
Width
8
You get
Leading zeros
3
Bit length
5
Binary
00010000
Most significant bit
4

Count leading zeros — CLZ, LZCNT, or a BSR-derived scan — is the number of zero bits that sit above the most significant one-bit of an unsigned integer in a fixed-width word. Compilers emit that count for integer log2, for normalizing a significand before a shift, and for finding the first set flag in a status register. This count leading zeros calculator accepts a non-negative integer as decimal digits, hexadecimal with a 0x prefix, binary with 0b, or octal with 0o, plus a word size of eight, sixteen, thirty-two, or sixty-four bits. It returns the CLZ count, the bit length of the magnitude, a width-padded binary string so you can see the leading zeros, and the zero-based index of the most significant set bit when the value is not zero. Zero is a first-class case: every bit is a leading zero, so the count equals the chosen width.

What count-leading-zeros means on a fixed-width word

Hardware count-leading-zeros instructions look at a register of a known width, not at an abstract mathematical integer. In an eight-bit word the value sixteen is the bit pattern 00010000: three zeros sit above the highest one, so CLZ is three. In a thirty-two-bit word the same magnitude is 00000000000000000000000000010000 and CLZ becomes twenty-seven, because twenty-four extra high zeros appear when you widen the register.

Algebraically the bit length of a positive integer is floor of log base two of the value plus one, and the leading-zero count is the word width minus that bit length. When the value is zero there is no most significant set bit at all; every position is a leading zero, so the count equals the width.

That is the convention of x86 LZCNT, ARM CLZ, RISC-V clz, and the compiler builtins __builtin_clz and leadingZeroBitCount: they report the full word size for a zero operand instead of leaving the result undefined the way older BSR encodings sometimes did. This capability encodes exactly that identity. The padded binary field is exactly width characters of zero and one with no 0b prefix, which makes the leading zeros visible without a second conversion step.

The formula field restates the log identity so generated docs and unit-test comments can quote the same sentence the calculator used.

What you can do with it

Compiler and VM CLZ oracles

Check integer log2, LZCNT lowering, and zero-operand behaviour against 8/16/32/64-bit hardware conventions in compiler and interpreter regression suites.

Register and flag normalization

Find how many high zeros sit above the highest set bit of a status or enable word before shifting a field into a canonical position.

Teaching bit length and log2

Let students compare handwritten padded binary and CLZ counts for a chosen word size without running a CPU simulator.

FAQ

How do I count the leading zero bits of an integer?

Send value (non-negative decimal, 0x, 0b, or 0o) and width (8, 16, 32, or 64).

Why must I choose 8, 16, 32, or 64 bits?

CLZ is defined on a fixed-width register. The same magnitude has a different leading-zero count in an 8-bit byte than in a 32-bit word; the closed enum matches common CPU and language widths.

What does count leading zeros return for zero?

The full width you chose: 8 for an 8-bit word, 64 for a 64-bit one. Every bit of zero is a leading zero, which matches x86 LZCNT, ARM CLZ and RISC-V clz instead of leaving the result undefined.

Can I enter the number in hexadecimal or binary?

Yes. Write plain decimal digits, hexadecimal with 0x, binary with 0b or octal with 0o. The number is read as unsigned and must fit in the chosen width, so a number that would need a ninth bit is refused at 8 bits.

How are leading zeros related to log2?

The bit length of a positive number is the floor of its base-two logarithm plus one, and the leading-zero count is the word width minus that bit length. For 16 in an 8-bit word the bit length is 5, so the count is 3.

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For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/dev/count-leading-zeros

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/dev/count-leading-zeros \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"value":"16","width":8}'

Example request

{
  "value": "16",
  "width": 8
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "dev.count_leading_zeros",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTPCodeMeaning
401unauthorizedMissing or invalid API key.
402insufficient_balanceYour balance doesn't cover the task price.
404unknown_typeThat task type doesn't exist.
429rate_limitedToo many requests. Use the webhook instead of polling.

Technical notes

What count-leading-zeros means on a fixed-width word

Bit numbering for the optional most_significant_bit field follows the usual programmer convention that bit zero is the least significant bit, so sixteen reports most_significant_bit four.

Input contract, widths, and error behaviour

POST a JSON body with two required fields. value is a non-negative integer written as a decimal digit string, a 0x hexadecimal literal, a 0b binary literal, or a 0o octal literal; a JSON number that is a safe non-negative integer is also accepted, and the aliases n, integer, and x map to the same field. width is the unsigned word size and must be one of the closed set eight, sixteen, thirty-two, or sixty-four — the widths of the common CLZ instructions — also accepted as bits or bit_width. The value is interpreted as unsigned and must fit in that many bits: sixteen is legal at eight bits, two hundred fifty-six is not, because it would need a ninth bit. Missing fields, empty strings, booleans, signs, fractional numbers, unknown prefixes, and a width outside the enum fail with invalid_input that names the rule, and those failures are not billed. On success the body echoes value as a canonical decimal string with no leading zeros (except the number zero itself) and width as a number, then exposes leading_zeros as the primary count, bit_length as the magnitude width (zero when the value is zero), and binary as the width-padded bit string. most_significant_bit is present only when the value is not zero; it is omitted rather than set to null so optional output stays honest. Example: value sixteen and width eight yields leading_zeros three, bit_length five, binary 00010000, and most_significant_bit four. Example: value zero and width thirty-two yields leading_zeros thirty-two, bit_length zero, and a string of thirty-two zero characters, with most_significant_bit absent.

Where a count-leading-zeros calculator earns its keep

Compiler and virtual-machine authors emit CLZ or a software fallback for integer log2, for finding the highest set flag, and for normalizing a mantissa before a floating-point style shift; they need an oracle that matches hardware on zero and on every supported width so regression suites do not silently accept an off-by-one in the log identity. Firmware and driver authors read status and enable registers and want the index of the highest pending bit without writing a portable clz helper in every language they touch. Cryptography and big-integer libraries normalize a limb before a left shift or before counting significant bits of a nonce, and a fixed-width calculator is the smallest way to check those helpers against eight- through sixty-four-bit cases including the all-zero limb. Educators teaching bitwise operators and IEEE-style normalization can give students a value and a width and compare handwritten padded binary plus the CLZ count against a deterministic service instead of a full ISA simulator. Keep requests small, pin leading_zeros and the padded binary string in tests, and you get reproducible CLZ results for SDKs, CMS snippets, and edge workers without standing up a local bit-scan library of your own.

Technical questions

What does count leading zeros return for zero?

leading_zeros equals the chosen width and bit_length is 0. most_significant_bit is omitted because no bit is set. That matches LZCNT, ARM CLZ, and compiler builtins.

Can I send hexadecimal or a JSON number?

Yes. value accepts decimal digits, 0x hex, 0b binary, 0o octal, or a safe non-negative JSON integer. The value must still fit in the chosen unsigned width.

What does the count leading zeros calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →