Converting from Binary to Decimal

Cisco Binary Numbers Game
A classic game for practicing converting numbers to and from Binary
Binary Bonanza!
A fun game for practicing converting numbers to and from Binary

There are 10 types of people in this world. Those who do understand binary and those who don't."

If the quote above doesn't make sense to you...then I'm sorry to say that you're one of the people who don't understand binary numbers. At the very least, you don't yet undersand how to read binary numbers. Hopefully, by the end of this web page the quote will make sense!

Part I. A General Method

The video below explains the general method for converting any base to a 'normal' base 10 number. Scroll down a bit to see a nice short cut that only works for converting a binary to a base 10 number.

Part II. A Quicker Way to Convert Binary to Decimal

This method leverages the fact that binary numbers only have a '1' or '0' in each digit which allows for quick conversions to base 10.

Practice I Problems

The long way. You can skip to the shortcut method here

Problem 1

Convert 10012 from binary to decimal.

Answer: 1+0+0+8 = 9

Problem 2

Convert 11002 from binary to decimal.

Answer: 0+ 0+ +4+8 = 12

Problem 3

Convert 11012 from binary to decimal.

Answer: 1+0+4+8 = 13

Practice II Problems

The shortcut method

Problem 1

Convert 101012 from binary to decimal.

Answer: 1 + 4 + 16 = 21

Problem 2

Convert 10101002 from binary to decimal.

Answer: 4 + 16 + 64 = 84

Problem 3

Convert 110100102 from binary to decimal.

Answer: 2 + 16 + 64 + 128 = 210

Problem 4

Convert 1010110102 from binary to decimal.

Answer: 2 + 8 + 16 + 64 + 256 = 346


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