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You convert binary numbers with a binary point into octal then same way you convert any number with a point in any other base to any other base.
Multiply or divide the number by its base until it is an integer, remembering how many times you multiplied or divided.
Iteratively divide the number by the new base, using the rules of arithmetic of the old base, recording the remainders, until the result is zero.
Represent the number in its new base by using the remainder in reverse order.
Divide or multiply the new number by the old base the same number of times you originally multiplied or divided it when you scaled it into an integer, using the rules of arithmetic of the new base. You are done.
Now, it turns out that converting binary to octal is easy and can be done on sight, because dividing by 10002 is the same as right shifting by three, and you don't have to prescale to an integer. Take the number 1101011.10011012. Simply group it into groups of three bits, starting at the binary point, giving you 001 101 011.100 110 1002. Note that I padded on the left and right with zeroes. Now you can convert by sight into octal. The result is 1534.4648.
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Floating point representation in binary why is it important to represent and how the decimal is placed in the binary?
It's a tricky area: Decimal numbers can be represented exactly. In contrast, numbers like 1.1 do not have an exact representation in binary floating point. End users typically would not expect 1.1 to display as 1.1000000000000001 as it does with binary floating point. The exactness carries over into arithmetic. In decimal floating point, 0.1 + 0.1 + 0.1 - 0.3 is exactly equal to zero. In binary floating point, the result is 5.5511151231257827e-017. While near to zero, the differences prevent reliable equality testing and differences can accumulate. For this reason, decimal is preferred in accounting applications which have strict equality invariants. So you have to be carefull how you store floating point decimals in binary. It can also be used in a fraction. It must be simplufied then reduced and multiplied.
Benefits of using floating point arithmetic over fixed point arithmetic in CPUs?
Fixed point number usually allow only 8 bits (32 bit computing) of binary numbers for the fractional portion of the number which means many decimal numbers are recorded inaccurately. Floating Point numbers use exponents to shift the decimal point therefore they can store more accurate fractional values than fixed point numbers. However the CPU will have to perform extra arithmetic to read the number when stored in this format. Fixed point number usually allow only 8 bits (32 bit computing) of binary numbers for the fractional portion of the number which means many decimal numbers are recorded inaccurately. Floating Point numbers use exponents to shift the decimal point therefore they can store more accurate fractional values than fixed point numbers. However the CPU will have to perform extra arithmetic to read the number when stored in this format.
What are the 3 parts to a binary numbering system?
point, based and place value
How do you convert 59 into decimal?
To convert the number 59 into a decimal, you simply write it as 59.0. This is because whole numbers are already considered decimals, with the decimal point being at the end of the number. So, 59 in decimal form is 59.0.
What is The actual numerical value assigned to nominal level variable?
The whole point of a nominal variable is that is has no numerical value associated with it. With a binary measure you can allocated the values 1 and 0 or +1 and -1 for observations where the attribute is present or absent. If there are more than 2 values that the nominal variable can take then you can allocate any numbers that you want but in all cases the numbers do not have a value: they are simply symbols which can help for sorting and for binary comparisons.
