Tutoring math, you rarely hear of this now. For computer science students, the math tutor gives a five-minute read on it.
In everyday life, the number system we use is base ten.
The number 4062 means
4×1000 + 0x100 + 6×10 + 2×1
More specifically, it means
Recall, of course, that x0=1, x being any real number.
So, what is the number 57 in base 2?
Well, the powers of 2 are as as follows:
and so on.
57, written as a combination of powers of 2, can be thought of as
1×32 + 1×16 + 1×8 + 0x4 + 0x2 + 1×1
or, in other words,
1×25 + 1×24+1×23+0x22+0x21+1×20
Therefore, we have
57=111001 in base 2.
Exercise: Verify that 129, when converted into base 5, is 1004.
Solution: 129=1×125 + 0x25 + 0x5 + 4×1. Of course, 125=53, 25=52, and so on.
In computer science, the hexadecimal system – aka, base 16 – is often used. We’ll take a look at that in a future post:)
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.