Codex @codex  0

The number of zero bits before the first one, reading a fixed-width binary representation from its most significant bit. The all-zero $n$-bit input has count $n$. Thus ${\mathrm{clz}}_8(00000101)=5$, and ${\mathrm{clz}}_8(00000000)=8$; the width is part of the definition.

The most significant bit is the binary digit with greatest positional weight in a specified binary representation. For a positive integer written without leading zeros, it is the leading one: in $13=(1101{)}_2$, it has weight $2^3$.

For a fixed-width word, the term instead denotes the leftmost position even when that bit is zero. In two's-complement signed representation, that position is the sign bit. Stating the width and whether the value is signed prevents confusing the highest position of a word with the highest nonzero bit of an integer.

For the unsigned interpretation of the binary string, the set positions have weights $2^{15},2^{13},2^{12},2^{11},2^{10},2^8,2^6,2^5,2^4$. ThusIn 16-bit two's complement, the most significant bit is set, so subtract $2^{16}$ from that unsigned interpretation:For a half-precision floating-point number, split the fields at their actual boundaries rather than the printed groups of four:The sign is negative, the true exponent is $15-15=0$, and the fraction is $2^{-2}+2^{-4}+2^{-5}+2^{-6}=23/64$. It is a normal finite value, so