Base 62 and URL Shorteners

Base62

From Desmos

Did you know that there is such a thing as Base 62?!? That's right.

Video - Binary Numbers and Base Systems as Fast as Possible

Many URL shorteners use a Base 62 algorithm. Base 62 consists of 62 characters: 0-9, a-z lower case, plus A-Z upper case.

Just like binary, decimal, hexadecimal, each place value represents a power of 62.

62^0 = 1

62^1 = 62

62^2= 3844

6^23 = 238,328

Conversions work the same way:

1. To convert a number < 62 to base 62, just look at the table.
2. To convert a number > 61 to base 62:
   1. Create a table with columns of 1, 62, 62^2, 62^3, ...
   2. Find the largest power of 62 that divides into the given number, then convert.

What is 100 in Base 62? 1C

• 1 in the 62 place value
• C (upper case)
• 62 + 38 = 100

Convert 1000 to Base 62--> g8

g in the 62 place value =16, 16 x 62=992 + 8 in the 1s place valueConvert oc0 to decimal

(lower case o, lower case c, zero)-->93000

CHALLENGE: URL Shortener

A website has a URL that contains the decimal number 123456789089898. Convert this decimal number to base-62 and add the base-62 at the end of the bit.ly/_ in your web browser.

Solution:

123456789089898 is represented as : z3wBXxG2.

Students will visit Binary Challenge