WHAT ARE THE RULES TO CONVERT A BINARY NUMBER INTO DECIMAL NUMBER.
Answers
Explanation:
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, and other professionals.
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.
Conversion from Binary to Decimal number system
There are mainly two methods to convert a binary number into decimal number − using positional notation, and using doubling. These methods are explained are as following below.
Using Positional Notation
Since number numbers are type of positional number system. That means weight of the positions from right to left are as 20, 21, 22, 23... and so on for the integer part and weight of the positions from left to right are as 2-1, 2-2, 2-3, 2-4... and so on for the fractional part.
Most Significant Bit (MSB) Binary Point Least Significant Bit (LSB)
22 21 20 2-1 2-2 2-3
4 2 1 0.5 0.25 0.125
Assume any unsigned binary number is bnb(n-1) ... b1b0.b-1b-2 ... b(m-1)bm. Then the decimal number is equal to the sum of binary digits (bn) times their power of 2 (2n), i.e., bnb(n-1) ... b1b0.b-1b-2 ... b(m-1)bm = bnx2n+b(n-1)x2(n-1)+ ... +b1x21+bx020+b-1x2-1+b-22-2+ ...
This is simple algorithm where you have to multiply positional value of binary with their digit and get the sum of these steps.
Example-1 − Convert binary number 11001010 into decimal number. Since there is no binary point here and no fractional part. So,
Position
Binary to decimal is,
= (11001010)2
= 1x27+1x26+0x25+0x24+1x23+0x22+1x21+0x20
= 128+64+0+0+8+0+2+0
= (202)10
Example-2 − Convert binary number 1010.1011 into decimal number. Since there is a binary point here with fractional part. So,
Fractional Part
Binary to decimal is,
= (1010.1011)2
= 1x23+0x22+1x21+0x20+1x2-1+0x2-2+1x2-3+1x2-4
= 8+0+2+0+0.5+0+0.125+0.0625
= (10.6875)10
Explanation:
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