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.