MODERN DEL
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salve Binary
Division
(iDolo) with (11)
Solve binary division (10010)2 with (11)2
Answers
Answer:
Binary Fractions
The binary numbering system is a base-2 numbering system which contains only two digits, a “0” or a “1”. Thus each digit of a binary number can take the “0” or the “1” value with the position of the 0 or 1 indicating its value or weighting. But we can also have binary weighting for values of less than 1 producing what are called unsigned fractional binary numbers.
Similar to decimal fractions, binary numbers can also be represented as unsigned fractional numbers by placing the binary digits to the right of the decimal point or in this case, binary point. Thus all the fractional digits to the right of the binary point have respective weightings which are negative powers of two, creating a binary fraction. In other words, the powers of 2 are negative.
So for the fractional binary numbers to the right of the binary point, the weight of each digit becomes more negative giving: 2-1, 2-2, 2-3, 2-4, and so on as shown.
Binary Fractions
binary fraction
etc, etc.
Thus if we take the binary fraction of 0.10112 then the positional weights for each of the digits is taken into account giving its decimal equivalent of:
binary fraction conversion
For this example, the decimal fraction conversion of the binary number 0.10112 is 0.687510.
Binary Fractions Example No1
Now lets suppose we have the following binary number of: 1101.01112, what will be its decimal number equivalent.
1101.0111 = (1×23) + (1×22) + (0×21) + (1×20) + (0×2-1) + (1×2-2) + (1×2-3) + (1×2-4)
= 8 + 4 + 0 + 1 + 0 + 1/4 + 1/8 + 1/16
= 8 + 4 + 0 + 1 + 0 + 0.25 + 0.125 + 0.0625 = 13.437510
Hence the decimal equivalent number of 1101.01112 is given as: 13.437510
So we can see that fractional binary numbers, that is binary numbers that have a weighting of less than 1 (20), can be converted into their decimal number equivalent by successively dividing the binary weighting factor by the value of two for each decrease in the power of 2, remembering also that 20 is equal to 1, and not zero.
Other Binary Fraction Examples
0.11 = (1×2-1) + (1×2-2) = 0.5 + 0.25 = 0.7510
11.001 = (1×21) + (1×20) + (1×2-3) = 2 + 1 + 0.125 = 3.12510
1011.111 = (1×23) + (1×21) + (1×20) (1×2-1) + (1×2-2) + (1×2-3)
= 8 + 2 + 1 + 0.5 + 0.25 + 0.125 =11.87510