Binary Numbers

Almost all of us deal with binary computers, even to the point that it seems redundant to say “binary.” When it gets down to the lowest levels, these deal with on or off, or what we’ve come to call 1 or 0. String enough of those 1s and 0s together, and I have the instructions to tell a computer to do something or the physical representation of data on a disk. And, although most of us don’t have to deal with computers at this level, some of this thinking has reached into high-level programming because we have to deal with lower levels at some point.

Consider, for instance, the arguments that I use with mkdir, chmod, or dbmopen to set the file mode (also known as permissions, but actually more than just that). Although I write the mode as a single base-8 number, its meaning depends on its particular bit pattern: