Related Bases 2

We do care about base 16

16 = 2⁴, so we can convert from base 2 to base 16 by using groups of 4

We use the name 'hexadecimal" for base 16, or "hex" for short

Why do we care about base 16? Imagine a binary representation like 10110101100110100010101101010:

• now imagine trying to copy it from your computer screen to a piece of paper that's behind you; that's pretty onerous
• now imagine doing the same with 16B3456A; I hope you think that's much less onerous
  • remember that 16 = 2⁴, so we need to bunch the binary into groups of 4 (starting at the right)
  • 1-0110-1011-0011-0100-0101-0110-1010
  • now convert each group separately from binary to hex, and we get 16B3456A
  • "what's with the A and B?" I hear you ask
    • well, we're converting to base 16, so we need 16 digits
    • 0-9 gives us 10 of them, so we need 6 more
    • ages ago somebody decided to use A-F; they seem to work, so we're sticking with them
    • A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15 (one less than our base)
    • you don't need to memorize these; just remember that A is the next one after 9 (i.e. 10)
    • you can count from there; why do you think that God put five fingers on your hand?
• let's look at a few of the separate conversions:
  • 0011 is 2 + 1 = 3
  • 0110 is 4 + 2 = 6
  • 0101 is 4 + 1 = 5
  • 1010 is 8 + 2 = 10, which is represented by the digit A
  • 1011 is 8 + 2 + 1 = 11, which is represented by the digit B
  • with a little practice, you can do them in your head