In my previous post, I talked about how I implemented a
binary counter with my Mojo FPGA board.
I am working on a follow-up post on implementing a reverse binary counter with
a switch that lets you change between the incrementing ( UP ) counter and
the decrementing ( DOWN ) counter.
I accidentally discovered a property of 8 bit numbers. It’s referred to as the
“Ones’ complement“.
When you add a number n between 0 and 255 to an 8-bit binary
representation of 0, the same number n subtracted from 255 will be the
binary inverse (bit
complement) of the first
number.
To demonstrate, let’s say we start with an 8-bit number at 0:
00000000
Now, we add 2:
00000010
OK, let’s look what happens when we have 255:
11111111
Now, let’s subtract 2:
11111101
So, comparing them, one above the other, we can see that they are inverse:
00000010
11111101
This is true for all numbers between 0 and 255 (the only assertion I can
personally make through observation).
So, in my original implementation of the reverse binary counter, I was using
two counters to keep up with the numbers; one that started at 0 and counted
up, and one that started at 255 and counted down.
As I switched between the two to test my design, I noticed the inversion
almost immediately. This might be a neat trick when you want to flash LED’s,
too.
I think a more efficient implementation to replace the DOWN counter is to
apply a simple inverter to each bit.
This is what happens when you learn in reverse. Rather than simply being
taught this in a ten minute aside from a lecture, I had to accidentally
discover it. I’m learning electronics engineering from a hobbyists
perspective, so I’m avoiding the theory and the complex math that makes it
actual engineering. I’m sure I’ll learn a lot more in the coming years.
This hobby never stops giving…