Bases

A base is a number system that assigns characters to values. The most common numbering systems found in computer science are:

  • Base-2 (more commonly known as binary)

    • Uses 0s and 1s to represent data

  • Base-10 (also known as denary)

    • Uses the numbers 0-9 to represent data.

  • Base-16 (also known as hexadecimal)

    • Uses 0-9 and the letters A-F to represent data.

There's also:

  • Base-8 (also known as octal)

    • Uses the numbers 0-7

  • Base32

    • Uses A-Z, 2-7 and =

  • Base 64

    • Uses A-Z, a-z, 0-9, + - =

  • Base85

    • Uses ASCII values 33-117

In normal, everyday use, we commonly use base 10 to represent numbers, as we don't often deal with large numbers on a day-to-day basis.

We can also represent values in different number systems, which can end up making some numbers look very odd to the untrained eye. For example:

  • 255 in denary

  • FF in hexadecimal

  • 1111 1111 in binary.

To show you all of these, I will now encode the message: {Hello! We are The WINRaRs} in Base 2, Base 8, Base 16, Base 32, Base 64, and Base 85.

  • Base 2

01111011 01001000 01100101 01101100 01101100 01101111 00100001 00100000 01010111 01100101 00100000 01100001 01110010 01100101 00100000 01010100 01101000 01100101 00100000 01010111 01001001 01001110 01010010 01100001 01010010 01110011 01111101

  • Base 8

173 110 145 154 154 157 41 40 127 145 40 141 162 145 40 124 150 145 40 127 111 116 122 141 122 163 175

  • Base 16

7b 48 65 6c 6c 6f 21 20 57 65 20 61 72 65 20 54 68 65 20 57 49 4e 52 61 52 73 7d

  • Base 32

PNEGK3DMN4QSAV3FEBQXEZJAKRUGKICXJFHFEYKSON6Q====

  • Base 64

e0hlbGxvISBXZSBhcmUgVGhlIFdJTlJhUnN9

  • Base 85

HUq^aCi:I>=(NL_Eb-@mBOr;f8PW/l;KI6

Notice how as we go along, the encoded strings get shorter? That's because we have more available slots to assign characters to.

You can even try and decrypt these messages here: https://gchq.github.io/CyberChef/#input=e0hlbGxvISBXZSBhcmUgVGhlIFdJTlJhUnN9

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