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Converting 10101101 to Decimal: Multiplying Each Column and Then Adding Them Together

Nov 26,2008 by alperen

image

Converting 10101101 to Decimal: Multiplying Each Column and Then Adding Them Together

Value associated with that digit or column

128

64

32

16

8

4

2

1

The number itself

1

0

1

0

1

1

0

1

Product of two numbers in the same column

128

0

32

0

8

4

0

1

Sum of all numbers in third row

173


The process is indeed simple, as long as you remember all the powers of 2! When you're working with IP addressing, you'll need to memorize all the powers of 2 up through 28, or 256. (The lowest powers of 2 are listed in Table B-5 later in this appendix.) The basic algorithm to convert binary to decimal can be summarized as follows:

Step 1.
Write down the powers of 2, in decimal, in the top row of a table, similar to Table B-4.

Step 2.
On the second line, write down the binary number that is to be converted, lining up each binary digit under the powers of 2.

Step 3.
Multiply each pair of numbers (the numbers in the same column) together and then total those products.

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