I’ve already presented and proved the rule for modular addition, so for a sense of completeness, but mostly to satisfy my OCD, now I’ll cover the rule for modular subtraction. When doing subtraction in modular arithmetic, the rule is:

If we subtract integer from integer and calculate the difference modulo , we get the same answer as if we had subtracted modulo from modulo and then calculated that difference modulo . Like the modular addition rule, this rule can also be expanded to include multiple integers.

Addition in modular arithmetic is much simpler than it would first appear thanks to the following rule:

This says that if we are adding two integers and and then calculating their sum modulo , the answer is the same as if we added modulo to modulo and then calculated that sum modulo . Note that this equation can be extended to include more than just two terms.

Source: DARPA Strategic Plan 2007

At 70 robot dog years-old – that’s 10 in human years – BigDog should’ve had a few more years of happily serving his masters ahead of him. Instead, the US Marines have pulled an Old Yeller on the unsuspecting robocanine, sending him to an early grave, or junkyard as the case may be.

Created in 2005, BigDog was the result of a collaborative effort between robotics design company Boston Dynamics, the NASA Jet Propulsion Laboratory (JPL), and researchers at Harvard University. Funding for BigDog came from the always forward-thinking Defense Advanced Research Projects Agency (DARPA) with development guidance and testing handled by the Marine Corps Warfighting Lab.

I’m almost ashamed to admit it, but my daughter got a robot for Christmas, and I had absolutely nothing to do with it. As a matter of fact, I was totally unfamiliar with Dot,  the cute, roughly 3.5 inch, sensor-packed, “brains of a robot” by San Mateo-based Wonder Workshop,  Inc. Now that I’ve had some hands on time with Dot and read up about her mobile sibling Dash, I have to say that I am impressed with these learning tools in disguise.