We saw that formula_35  Hence after determining a representation of 0.375 as formula_36 we can proceed as above:   From these we can form the resulting 32-bit IEEE 754 binary32 format representation of real number 0.375:  These examples are given in bit "representation", in hexadecimal and binary, of the floating-point value. This includes the sign, (biased) exponent, and significand. By default, 1/3 rounds up, instead of down like double precision, because of the even number of bits in the significand. The bits of 1/3 beyond the rounding point are codice_1 which is more than 1/2 of a unit in the last place. Encodings of qNaN and sNaN are not specified in IEEE 754 and implemented differently on different processors. The x86 family and the ARM family processors use the most significant bit of the significand field to indicate a quiet NaN. The PA-RISC processors use the bit to indicate a signalling NaN. We start with the hexadecimal representation of the value, , in this example, and convert it to binary:  then we break it down into three parts: sign bit, exponent, and significand. We then add the implicit 24th bit to the significand:   and decode the exponent value by subtracting 127:   Each of the 24 bits of the significand (including the implicit 24th bit), bit 23 to bit 0, represents a value, starting at 1 and halves for each bit, as follows:  The significand in this example has three bits set: bit 23, bit 22, and bit 19. We can now decode the significand by adding the values represented by these bits. Then we need to multiply with the base, 2, to the power of the exponent, to get the final result:  Thus  This is equivalent to: where is the sign bit, is the exponent, and is the significand. The design of floating-point format allows various optimisations, resulting from the easy generation of a base-2 logarithm approximation from an integer view of the raw bit pattern. Integer arithmetic and bit-shifting can yield an approximation to reciprocal square root (fast inverse square root), commonly required in computer graphics. Microsoft adCenter Labs  Microsoft adCenter Labs (a.k.a. adlabs), is an applied research group at Microsoft that supports Microsoft adCenter. Microsoft adCenter (formerly MSN adCenter), is the division of the Microsoft Network (MSN) responsible for MSN's advertising services.