# 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

4×10^{3}+0x10^{2}+6×10^{1}+2×10^{0}

Recall, of course, that x^{0}=1, x being any real number.

So, what is the number 57 in base 2?

Well, the powers of 2 are as as follows:

2^{0}=1

2^{1}=2

2^{2}=2×2=4

2^{3}=2x2x2=8

2^{4}=2x2x2x2=16

2^{5}=32

2^{6}=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,

1×2^{5} + 1×2^{4}+1×2^{3}+0x2^{2}+0x2^{1}+1×2^{0}

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=5^{3}, 25=5^{2}, 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.