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Converting from Binary to Decimal

"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.

1001 from binary to decimal

Answer: 1 + 0 + 0 + 8 = 9.

Problem 2

Convert 11002 from binary to decimal.

1100 from binary to decimal

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

Problem 3

Convert 11012 from binary to decimal.

1101 from binary to decimal

Answer: 1 + 0 + 4 + 8 = 13.

Practice II Problems

The shortcut method.

Problem 1

Convert 101012 from binary to decimal.

10101 from binary to decimal

Answer: 1 + 4 + 16 = 21.

Problem 2

Convert 10101002 from binary to decimal.

1010100 from binary to decimal

Answer: 4 + 16 + 64 = 84.

Problem 3

Convert 110100102 from binary to decimal.

11010010 from binary to decimal

Answer: 2 + 16 + 64 + 128 = 210.

Problem 4

Convert 1010110102 from binary to decimal.

101011010 fom binary to decimal

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


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