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This is the Binary32 format from IEEE-754-2008.

To convert a decimal to binary real start by checking for zero. If so, the answer is all zeroes. Then record the sign and make the number positive. Then create an exponent with an initial value of 127. Iteratively multiply or divide the number by two, while decrementing or incrementing the exponent, until the number is greater than or equal to 1, and less than 2. Throw away the high order bit, by subtracting one from the number, as it will always be one, and we can imply it in the result. Multiply the number by 223, and add 0.5, to construct a rounded integer mantissa of 23 bits in length. Assemble the sign bit, 8 bit exponent, and 23 bit mantissa together. Note that exponents of 255 and 0 are special and are interpreted differently, so the proper range of exponent is 1 to 254.

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For more information of other formats covered under the specification, please see the second Related Link below.

Q: How do you convert decimal to binary of real values?

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One-complement applies to binary values, not decimal values. Therefore when we say the ones-complement of a decimal value we mean convert the value to binary, invert all the bits (the ones-complement), then convert the result back to decimal. For example, the decimal value 42 has the following representation in 8-bit binary: 00101010 If we invert all the bits we get 11010101 which is 213 decimal. Thus 213 is the ones-complement of 42, and vice versa. However, it's not quite as straightforward as that because some (older) systems use ones-complement notation to represent signed values, such that 11010101 represents the decimal value -42. The problem with this notation is that the ones-complement of 00000000 is 11111111 which means the decimal value 0 has two representations, +0 and -0 respectively. In the real-world, zero is neither positive nor negative. To resolve this problem, modern systems use twos-complement to represent signed values. The twos-complement of any value is simply the ones-complement plus one. Thus the ones-complement of 42 becomes -43, therefore the twos-complement of 42 is -43+1 which is -42. Thus -42 is represented by the binary value 11010110 in twos-complement notation. With twos-complement, there is only one representation for the value 0. This is because the ones-complement of 00000000 is 11111111 and if we add 00000001 we get 00000000. Note that we don't get 100000000 because the result cannot have any more bits than were in the original value. When an "overflow" occurs, we cycle back to zero. As a result, incrementing and decrementing signed values has exactly the same logic as incrementing or decrementing unsigned values and flipping the sign of any value is only slightly more complicated by the extra addition operation. However, flipping the sign of a value is a much rarer operation than counting so the cost is trivial compared to the cost of counting operations using ones-complement (because there are two values for zero). Note that ones-complement notation allows an 8-bit value to store signed values in the range -127 to +127, whereas twos-complement allows a range of -128 to +127 (through the elimination of the extra zero). But in unsigned notation, both allow the same range: 0 to 255. Although we rarely encounter ones-complement notation, it is important to keep in mind that not all systems use twos-complement notation, particularly when working with low-level but portable programming languages. This is the reason why both the C and the C++ standards state that the range of an 8-bit signed value is only guaranteed to store values in the range -127 to +127.

Yes because there is no real practical use for a binary tree other than something to teach in computer science classes. A binary tree is not used in the real world, a "B tree" is.

There is no real answer to this. Binary codes can be any length. The minimum length is 1 byte.

This is not a perfect program, but it will get you started in the right direction. Works for any INTEGER up to "some" power of 2 (decimals kill the program). PROGRAM binary IMPLICIT NONE INTEGER remainder, quotient, n, int_input, answer REAL input, dec_input WRITE(*,*) 'Input a number to convert to binary' READ(*,*) input int_input = input dec_input = input - int_input dec_input = abs(dec_input) quotient = abs(input) DO WHILE (dec_input==0) n = 0 answer = 0 DO WHILE (quotient>1) remainder = mod(quotient,2) quotient = quotient/2 answer = answer+remainder*10.**n n = n+1 END DO IF (input<0) answer = -answer answer = answer + quotient*10.**n WRITE(*,"(a,i31)") 'Your answer in binary is:',answer END DO END PROGRAM binary

binary code(computer science) A code in which each allowable position has one of two possible states, commonly 0 and 1; the binary number system is one of many binary codes.Source: http://www.answers.com/binary+code?cat=technology

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I don't want to try. Pi has been calculated to far higher values than a million decimal places. However more than about forty places have no practical use in the real universe.

Single Precision, called "float" in the 'C' language family, and "real" or "real*4" in Fortan. This is a binary format that occupies 32 bits (4 bytes) and its significand has a precision of 24 bits (about 7 decimal digits). Double Precision called "double" in the C language family, and "double precision" or "real*8" in Fortran. This is a binary format that occupies 64 bits (8 bytes) and its significand has a precision of 53 bits (about 16 decimal digits). Regards, Prabhat Mishra

One-complement applies to binary values, not decimal values. Therefore when we say the ones-complement of a decimal value we mean convert the value to binary, invert all the bits (the ones-complement), then convert the result back to decimal. For example, the decimal value 42 has the following representation in 8-bit binary: 00101010 If we invert all the bits we get 11010101 which is 213 decimal. Thus 213 is the ones-complement of 42, and vice versa. However, it's not quite as straightforward as that because some (older) systems use ones-complement notation to represent signed values, such that 11010101 represents the decimal value -42. The problem with this notation is that the ones-complement of 00000000 is 11111111 which means the decimal value 0 has two representations, +0 and -0 respectively. In the real-world, zero is neither positive nor negative. To resolve this problem, modern systems use twos-complement to represent signed values. The twos-complement of any value is simply the ones-complement plus one. Thus the ones-complement of 42 becomes -43, therefore the twos-complement of 42 is -43+1 which is -42. Thus -42 is represented by the binary value 11010110 in twos-complement notation. With twos-complement, there is only one representation for the value 0. This is because the ones-complement of 00000000 is 11111111 and if we add 00000001 we get 00000000. Note that we don't get 100000000 because the result cannot have any more bits than were in the original value. When an "overflow" occurs, we cycle back to zero. As a result, incrementing and decrementing signed values has exactly the same logic as incrementing or decrementing unsigned values and flipping the sign of any value is only slightly more complicated by the extra addition operation. However, flipping the sign of a value is a much rarer operation than counting so the cost is trivial compared to the cost of counting operations using ones-complement (because there are two values for zero). Note that ones-complement notation allows an 8-bit value to store signed values in the range -127 to +127, whereas twos-complement allows a range of -128 to +127 (through the elimination of the extra zero). But in unsigned notation, both allow the same range: 0 to 255. Although we rarely encounter ones-complement notation, it is important to keep in mind that not all systems use twos-complement notation, particularly when working with low-level but portable programming languages. This is the reason why both the C and the C++ standards state that the range of an 8-bit signed value is only guaranteed to store values in the range -127 to +127.

Yes because there is no real practical use for a binary tree other than something to teach in computer science classes. A binary tree is not used in the real world, a "B tree" is.

There is no real answer to this. Binary codes can be any length. The minimum length is 1 byte.