# What does “$<\!\!<\!\!<$” mean?

What does the symbol $<\!\!<\!\!<$ mean? It is normally followed by a number. An example:

It would be appreciated if you could explain it in fairly basic terms.

$$x<\!\!<\!\!<k$$ normally means cyclic rotation of a bit string $x$ to the left by $k$ bits.
• Small side notes with regards to programming: 1) >>> in Java means shift right without sign extension (Java only has signed numbers, so the first bit is the sign). It's not rotation for that language. Other languages may have similar issues, check your operator 2) If you have a register / variable $x$ with $n$ bits then rotating left $k$ bits is the same as rotating right $n - k$ bits. And usually you can also rotate left $y \cdot n + k$ bits of course (if you rotate $n$ bits $n$ places then you're back where you started from) . – Maarten Bodewes Feb 18 '17 at 22:32