Binary to Decimal

“There’s 10 types of people in the word, those who know how to read binary, and those who don’t.”

Sometimes in the tech world, it is handy to understand how to read and convert binary numbers to our regular decimal system. Let’s list what we know about decimals first:

  • There are 10 digits to choose from.
  • A digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
  • Each number can be represented as a sum of 10^x where x is the 10’s place the digit is in.

Let’s break down a simple example:

  • 1024
  • = 1000       + 0             + 20           + 4
  • = 1*(10^3) + 0*(10^2) + 2*(10^1) + 4*(10^0)

We can say similar things about Binary:

  • There are 2 digits to choose from.
  • A digit can be 0 or 1.
  • Each number can be representedas a sum of 2^x where x is the 2’s place the digit is in.

Let’s break down this example:

  • 11011
  • = 10000    + 1000      + 0           + 10         + 1
  • = 1*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0)
  • = 1*16      + 1*8       + 0*4        + 1*(2)     + 1*1
  • = 16          + 8          + 0            + 2           + 1
  • = 25

Voila! We just converted into base 10 decimal from binary without knowing it!

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