We usually write numbers in base 10, but you can write numbers in any base.

Let’s write the number 103 in 3 different bases:

base 10: 103
(powers of 10)

1 x 100 = 100
0 x 10 = 0
3 x 1 = 3
= 103

base 2: 1100111
(powers of 2)

1 x 64 = 64
1 x 32 = 32
0 x 16 = 16
0 x 8 = 8
1 x 4 = 4
1 x 2 = 2
1 x 1 = 1
64 + 32 + 16 + 8 + 4 + 2 + 1 = 103

base 3: 67
(powers of 16)

6 x 16 = 96
7 x 1 = 7
96 + 7 = 103

base 2, 10, and 16 are the main bases we use on computers

• base 2 is called binary
• base 10 is called decimal
• base 16 is called hexadecimal

how to convert from base 10 to base 2

Let’s convert 19! We’ll start on the right and move left. 1. Divide by 2: ¹⁹⁄₂ = 9 remainder 1 2. Write the remainder (1) below, and 9 on the left 3. Repeat

answer: 10011!

person: but in real life I’d just ask a computer