Have you seen this symbol?

Question

I am studying Digital Design and Computer Architecture by David Money Harris and Sarah L. Harris.

My professor asked searching the name of this symbol.

He says this symbol means to select the smallest number which is bigger than $\log N$.

Please help me.

Answer 1

This is the ceiling function $\lceil x\rceil$ defined (for $x\in\mathbb R$) to be the smallest integer $\geq x$.

There is also the corresponding floor function $\lfloor x\rfloor$, which is the largest integer $\leq x$.

Answer 2

I have not seen that symbol, but I would guess it's just a typographical variant of the ceiling symbol $\lceil x \rceil$.

He says this symbol means [to] select the smallest number which [is] bigger than $\log N$.

Okay, so it is the ceiling symbol $\lceil x \rceil$ with $x$ being $\log N$. If $x$ is a real number, then $\lceil x \rceil$ is the largest integer greater than or equal to $x$.

Let's say $N \approx 20.0855369231$. Then $\log N = 3$ and so $\lceil 3 \rceil = 3$. Or by $\log$ do you mean the base 10 logarithm rather than the natural logarithm? Then we have $\log_{10} N \approx 1.3028834457$ and $\lceil 1.3028834457 \rceil = 2$.

In this context you probably won't be applying the logarithm function to negative numbers, but you might apply the ceiling function to negative numbers. In that case, you have to be careful not to get confused about direction. For example, $\lceil -\pi \rceil = -3$, not $-4$.