Here you will be learning about arithmetic circuits from the ground up. In theory you can look at each unit independently, with the exception of the multipliers, which require you to know about carry-save adders, and some multipliers build upon the architecture of existing adders. But learning from adders to the FPU in that order feels natural, at least to me, and not jut because of difficulty. Multipliers build their architecture from adders. Similarly, dividers depend on subtraction. FPUs depend on adders and multipliers, as do systolic architectures and DSPs.
Barrel shifters differ from one another on a transistor level, even if almost all of the shifter architectures are implemented with pass transistors. If you’re writing HDL code, none of this matters to you, so the article will mostly be used just to sate your curiosity.
Warning: my master’s thesis is about systolic architectures. If there
is some information that you can’t find anywhere else online, it’s
probably because I made it the fuck up it’s something that I
got out of my research.