# 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

4×103+0x102+6×101+2×100

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:

20=1

21=2

22=2×2=4

23=2x2x2=8

24=2x2x2x2=16

25=32

26=64

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.