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Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's byte order. Rather, it is a property of the numeric value in binary itself. This is often utilized in programming via bit shifting: A value of 1 << n corresponds to ...
While a single bit, on its own, is able to represent only two values, a string of bits may be used to represent larger values. For example, a string of three bits can represent up to eight distinct values as illustrated in Table 1. As the number of bits composing a string increases, the number of possible 0 and 1 combinations increases ...
Significand precision: 237 bits (236 explicitly stored) The format is written with an implicit lead bit with value 1 unless the exponent is all zeros. Thus only 236 bits of the significand appear in the memory format, but the total precision is 237 bits (approximately 71 decimal digits: log 10 (2 237) ≈ 71.344). The bits are laid out as follows:
Logarithmic number systems (LNSs) represent a real number by the logarithm of its absolute value and a sign bit. The value distribution is similar to floating point, but the value-to-representation curve (i.e., the graph of the logarithm function) is smooth (except at 0). Conversely to floating-point arithmetic, in a logarithmic number system ...
The full decimal significand is then obtained by concatenating the leading and trailing decimal digits. The 10-bit DPD to 3-digit BCD transcoding for the declets is given by the following table. b 9 … b 0 are the bits of the DPD, and d 2 … d 0 are the three BCD digits.
Thus only 23 fraction bits of the significand appear in the memory format, but the total precision is 24 bits (equivalent to log 10 (2 24) ≈ 7.225 decimal digits) for normal values; subnormals have gracefully degrading precision down to 1 bit for the smallest non-zero value. The bits are laid out as follows:
If the 2 bits after the sign bit are "11", then the 8-bit exponent field is shifted 2 bits to the right (after both the sign bit and the "11" bits thereafter), and the represented significand is in the remaining 21 bits. In this case there is an implicit (that is, not stored) leading 3-bit sequence "100" in the true significand:
The value of n >>> s is n right-shifted s bit positions with zero-extension. In bit and shift operations, the type byte is implicitly converted to int. If the byte value is negative, the highest bit is one, then ones are used to fill up the extra bytes in the int. So byte b1 =-5; int i = b1 | 0x0200; will result in i == -5.