Number Representations in Computer Hardware

Welcome to arguably the most fundamental component of computer design: how numbers are represented in hardware!

We all know that modern computers operate on binary numbers and are extremely efficient at doing so. But this was not always the case. What's more, many tech giants today, including Microsoft, Nvidia, Intel, Arm, and Tesla, are revisiting how they encode numbers in hardware to squeeze out every last bit of performance.

As Shakespeare would have it, "that which we call a rose by any other name would smell just as sweet." But in the world of computers, the way we represent a number in hardware can mean the difference between a blazing fast machine and a costly $475 million bug – Pentium 4, anyone?