This is the kind of thing that is very misleadingly true. If you simply take growth in computing power and extrapolate to the end of the century, and compare it to the current best estimate of human brain computing power, then yes, we'll get there.

But 1) that is an estimate of human brain computing power, based on number of neurons and possible connections. We have no idea if that is really a valid unit of computing "power." Do brain only compute things via voltage thresholds across synapses? Then yes, maybe this is an accurate estimate. But there are a whole lot of subcellular signal cascades happening at molecular levels we can't even begin to count and we have no idea whether or not those are also computing something accessible to the rest of the brain. 2) Matching the computing power of a brain doesn't mean you can emulate it. Emulating something requires knowing the target architecture and software. It is possible we can figure out exactly what a brain is doing to an accurate enough level to emulate it by the end of the century, but we certainly don't know how to do that right now, even if we had the computing power. Remote imaging techniques are not nearly good enough (because again, so many of the processes are subcellular) and you can't open up a brain without destroying it. This is actually a much broader problem in biology and we have figured out ways to partially dissect some animals while still keeping them alive long enough to figure out how a system works in vivo, but doing that with a brain is not something we have ever come remotely close to doing and there isn't really any ethical way to even think of how we can try to figure it out.