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Leading Zero Counter

Enter an integer and bit width to count its leading zero bits.

How it is calculated

Enter a non-negative decimal integer and a bit width from 1 to 64 (32 if left empty). The tool finds the bit length, the number of binary digits needed without leading zeros, by shifting the value right until it reaches zero. Then leading zeros = width − bit length. Zero has a bit length of 0, so all bits are leading zeros. The binary string is padded to the full width. A fractional value is cut to its integer part (22.9 becomes 22), while negative numbers, hexadecimal text such as 0x16 and a value that needs more bits than the chosen width give no result. Everything is treated as unsigned, so there is no sign bit.

Worked example

Value 1000 in a 16-bit register. In binary 1000 is 1111101000, which is 10 digits, so the bit length is 10. Leading zeros: 16 − 10 = 6. Padded to 16 bits the pattern is 0000001111101000: six zeros, then the ten bits of the number. As a check, 2⁹ = 512 ≤ 1000 < 1024 = 2¹⁰, so the highest set bit is bit 9 and floor(log₂ 1000) = 9, which is the bit length minus one.

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Common mistakes

  • Forgetting that the answer depends on the width. The same value 1000 has 6 leading zeros in 16 bits but 22 in 32 bits.
  • Typing hexadecimal or binary text (0x3E8, 1111101000). The input is read as a decimal number, so convert it first.
  • Entering a value that is too large for the width, such as 300 with 8 bits. Instead of wrapping around, the tool returns no result, so choose a wider width.
  • Using negative numbers expecting two's complement. This counts unsigned values only; -1 is rejected rather than shown as all ones.
  • Mixing up leading zeros with bit length or the index of the highest bit. Leading zeros = width − bit length, and the highest set bit's index is bit length − 1.

About this calculator

Counting leading zeros (CLZ) means counting how many zero bits appear before the first 1-bit in a number's binary representation at a fixed bit width — for example, the 8-bit value 00010110 has 3 leading zeros. It's closely related to finding a number's bit-length and its floor(log₂(n)) value, since the position of the first set bit determines both.

Low-level programmers use CLZ for fast integer log2 calculations, normalizing floating-point mantissas, and bit-manipulation tricks in performance-critical code, which is why most modern CPUs implement it as a single hardware instruction (x86's LZCNT, ARM's CLZ) rather than requiring a software loop — this calculator lets you check that instruction's result by hand.

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Comments (1)

  • Editorial team

    The answer depends on the register width you choose, so pick the width of your target type. Zero is a special case: in 8 bits it returns 8 leading zeros with a bit length of 0, while 255 returns none. Hardware differs here, because some instructions leave the count for zero undefined and others return the full width. For a quick log2, floor(log2 n) is the width minus 1 minus this count. Which language or architecture are you working in?

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