CTZ, or Count Trailing Zeros, returns the number of consecutive zero bits starting from the least significant bit up to the first 1 bit. The value 48 is 110000 in binary, so it has four trailing zeros.

How does CTZ relate to powers of two?

The trailing zero count is the exponent of the largest power of two that divides the number evenly. If CTZ is 4, then 2 to the 4th, which is 16, divides the value and 32 does not.

What is CTZ used for?

It powers the binary GCD algorithm, memory alignment checks, finding the lowest set bit in a bitmask scheduler, and isolating individual flags. Hardware exposes it as TZCNT on x86 or RBIT plus CLZ on ARM.

It is undefined, because zero has no set bit to stop at, so every bit is a trailing zero. This tool reports that case explicitly rather than returning a misleading number.

Does the register width matter for CTZ?

No, unlike leading zeros. Trailing zeros are counted from the bottom up to the first set bit, so the answer does not depend on how wide the register is, only on the value itself.

Trailing Zeros Counter (CTZ)

Count Trailing Zeros (CTZ) tells you how many zero bits sit below the lowest set bit of a number. Unlike leading zeros it is independent of register width, and it equals the exponent of the largest power of two dividing the value. This tool computes it for any non-negative integer in decimal, hex, or binary.

How it works

The tool isolates the lowest set bit by shifting the value right while the bottom bit is zero, counting the shifts:

count = 0
while (value & 1) == 0:
    value >>= 1
    count += 1

That count is the position of the lowest set bit (0-indexed from the right) and the exponent k such that 2^k divides the original number but 2^(k+1) does not. Trailing zeros of zero are undefined because no set bit exists to halt the loop, so the tool flags that case rather than looping forever.

Example and notes

The decimal value 48 is 110000 in binary, with four trailing zeros, so CTZ is 4 and 2^4 = 16 is the largest power of two dividing it. CTZ drives the binary GCD (Stein’s) algorithm, lets allocators verify pointer alignment, and finds the next ready task in a bitmask scheduler. On x86 it is the TZCNT instruction; on ARM it is computed by bit-reversing and applying CLZ. This calculator uses BigInt so the input can be arbitrarily large.