How do you convert Binary to Decimal? | What is decimal equivalent? | How is decimal calculated?
How do you convert binary to decimal? | What is decimal equivalent? | How is decimal calculated?
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Binary is the simplest kind of number system that uses only two digits of 0 and 1 (i.e. value of base 2). Since digital electronics have only these two states (either 0 or 1), so binary number is most preferred in modern computer engineer, networking and communication specialists, etc.
Whereas Decimal number is most familiar number system to the general public. It is base 10 which has only 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
How to Convert Binary to Decimal
There are two methods to apply a binary to decimal conversion. The first one uses positional representation of the binary, which is described above. The second method is called double dabble and is used for converting longer binary strings faster. It doesn’t use the positions.
Method :
Step 1: Write down the binary number.
Step 2: Starting with the least significant digit (LSB - the rightmost one), multiply the digit by the value of the position. Continue doing this until you reach the most significant digit (MSB - the leftmost one).
Step 3: Add the results and you will get the decimal equivalent of the given binary number.
Now, let's apply these steps to, for example, the binary number above, which is (10100)2
Step 1: Write down (10100)2 and determine the positions, namely the powers of 2 that the digit belongs to.
Step 2: Represent the number in terms of its positions. (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1+0*2^0)
Step 3: (1 * 16) + (0 * 8) + (1 * 4) +(0 * 2)+ (0 * 1) = 16+ 0 + 4 + 0 +0= 20
Therefore, (10100)2 = (20)10
Example : Convert binary number 1100100 into decimal number.
Binary to decimal is,
= (1100100)2
= 1x2^6+1x2^5+0x2^4+0x2^3+1x2^2+0x2^1+0x2^0
= 64+32+0+0+4+0+0
= (100)10
What are Binary Numbers?
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Keywords:
Number System
Binary Number System
Decimal Number System
Octal Number System
Hexadecimal Number System
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Decimal to Hexadecimal Conversion
Hexadecimal to Binary Conversion
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