How to Convert a Binary Number to a Decimal Number

Guest Author - Cathy Spearmon

Converting a Binary Number to a Decimal Number

In order to find topics for articles, I quite often review my site searches to determine those topics that are of interest to my site visitors. During my most recent review, I noticed that quite a number of searches were done on the topic of converting a binary number to a decimal number. So, for those of you who are interested in this topic, I've provided some basic steps in performing the conversion.

1. Start with the last digit and multiply that digit with 2^0. Note that the power of 0 of any number is always 1.

2. Continue working from right to left multiply each digit with an incremental increasing power of 2 (i.e. 2^1, 2^2, 2^3, 2^4, etc).

3. Repeat step 2 until all digits have been multiplied.

4. Add the end result of each worked power of 2 for a final answer.

Example: Convert Binary 1010 to a Decimal

Multiply	Result
0 * (2^0)	0
1 * (2^1)	2
0 * (2^2) or 2*2	0
1 * (2^3) or 2*2*2	8
Answer	10

Example: Convert Binary 11011 to a Decimal

Multiply	Result
1 * (2^0)	1
1 * (2^1)	2
0 * (2^2) or 2*2	0
1 * (2^3) or 2*2*2	8
1 * (2^4) or 2*2*2*2	16
Answer	27

Example Convert Binary 111010 to a Decimal

Multiply	Result
0 * (2^0)	0
1 * (2^1)	2
0 * (2^2) or 2*2	0
1 * (2^3) or 2*2*2	8
1 * (2^4) or 2*2*2*2	16
1 * (2^5) or 2*2*2*2*2	32
Answer	58

Example Convert Binary 1010010 to a Decimal

Multiply	Result
0 * (2^0)	0
1 * (2^1)	2
0 * (2^2) or 2*2	0
0 * (2^3) or 2*2*2	0
1 * (2^4) or 2*2*2*2	16
0 * (2^5) or 2*2*2*2*2	0
1 * (2^6) or 2*2*2*2*2*2	64
Answer	82