Single-precision floating point representation converter

It will convert both normal and subnormal numbers, and will convert numbers that overflow to infinity or underflow to zero. The resulting floating-point number can be displayed in ten forms: in decimal, in binary, in normalized decimal scientific notation, in normalized binary scientific notation, as a normalized decimal times a power of two, as a decimal integer times a power of two, as a decimal integer times a power of ten, as a hexadecimal floating-point constant, in raw binary, and in raw hexadecimal.

Each form represents the exact value of the floating-point number. This converter will show you why numbers in your computer programs, like 0. The mantissa also known as significand or fraction is stored in bits An invisible leading bit i.

As a result, the mantissa has a value between 1. If the exponent reaches binary , the leading 1 is no longer used to enable gradual underflow. If the exponent has minimum value all zero , special rules for denormalized values are followed. The exponent value is set to 2 and the "invisible" leading bit for the mantissa is no longer used. Note: The converter used to show denormalized exponents as 2 and a denormalized mantissa range [ This is effectively identical to the values above, with a factor of two shifted between exponent and mantissa.

However this confused people and was therefore changed Not every decimal number can be expressed exactly as a floating point number.

This can be seen when entering "0. The hex representation is just the integer value of the bitstring printed as hex. Don't confuse this with true hexadecimal floating point values in the style of 0xab. This source code for this converter doesn't contain any low level conversion routines. The conversion between a floating point number i. The following figure shows all the parts of the single precision representation. Single-precision floating point number representation. As shown in the above figure, the single-precision representation has 1 bit sign S , 8 bits exponent E , and 23 bits mantissa F.

Just to clarify the confusion, the given binary number is not represented in any signed number format. It is represented the way we write decimal numbers; negative number with a minus sign and positive number without any sign. Exponent E : The size of exponent is 8 bits, and the range of exponent that can be represented in this case is from to This indicates, that very large positive and negative numbers can be represented by using single-precision floating point format.

The exponent is represented as a biased exponent. The biased form of the exponent is derived by adding to the original exponent. The objective of the exponent bias is to convert the exponent to always a positive number, and therefore we do not need another sign-bit for the exponent part.