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A common example is the Data General Nova, which was a 16-bit design that performed 16-bit math as a series of four 4-bit operations. 4-bits was the word size of a widely available single-chip ALU and thus allowed for inexpensive implementation. Using the definition being applied to the 68000, the Nova would be a 4-bit computer, or 4/16.
The advantage over 8-bit or 16-bit integers is that the increased dynamic range allows for more detail to be preserved in highlights and shadows for images, and avoids gamma correction. The advantage over 32-bit single-precision floating point is that it requires half the storage and bandwidth (at the expense of precision and range). [5]
where p is the number of significant bits in the binary format, e.g. 237 bits for binary256. When using a decimal floating-point format, the decimal representation will be preserved using: 7 decimal digits for decimal32, 16 decimal digits for decimal64, 34 decimal digits for decimal128.
Bfloat16 is designed to maintain the number range from the 32-bit IEEE 754 single-precision floating-point format (binary32), while reducing the precision from 24 bits to 8 bits. This means that the precision is between two and three decimal digits, and bfloat16 can represent finite values up to about 3.4 × 10 38 .
For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit. The fractional bits continue the pattern set by the integer bits. The next bit is the half's bit, then the quarter's bit, then the ⅛'s bit, and so on. For example:
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 (binary64), usually used to represent the "double" type in the C language family. This is a binary format that occupies 64 bits (8 bytes) and its significand has a precision of 53 bits (about 16 ...
In the binary integer decimal (BID) encoding, it is encoded as a binary number. Format ... 16 34 Combination bits 11 13 17 Exponent bits 8 10 14 Bias 101 398
In the binary system, each bit represents an increasing power of 2, with the rightmost bit representing 2 0, the next representing 2 1, then 2 2, and so on. The value of a binary number is the sum of the powers of 2 represented by each "1" bit. For example, the binary number 100101 is converted to decimal form as follows: