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An integral type with n bits can encode 2 n numbers; for example an unsigned type typically represents the non-negative values 0 through 2 n − 1. Other encodings of integer values to bit patterns are sometimes used, for example binary-coded decimal or Gray code, or as printed character codes such as ASCII.
Signed range (two's complement representation) Unsigned range 1 byte 8 bits Byte, octet, minimum size of char in C99( see limits.h CHAR_BIT) −128 to +127 0 to 255 2 bytes 16 bits x86 word, minimum size of short and int in C −32,768 to +32,767 0 to 65,535 4 bytes 32 bits
Thus, Q12 means a signed integer with any number of bits, that is implicitly multiplied by 2 −12. The letter U can be prefixed to the Q to denote an unsigned binary fixed-point format. For example, UQ1.15 describes values represented as unsigned 16-bit integers with an implicit scaling factor of 2 −15, which range from 0.0 to (2 16 −1)/2 ...
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]
For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535. For this sign representation method, the leftmost bit ( most significant bit ) denotes whether the value is negative (0 for positive or zero, 1 for negative).
The minimum size for char is 8 bits, the minimum size for short and int is 16 bits, for long it is 32 bits and long long must contain at least 64 bits. The type int should be the integer type that the target processor is most efficiently working with.
Programs that process years as 16-bit values may encounter problems dealing with either the year 32,768 or 65,536, depending on whether the value is treated as a signed or unsigned integer. For the year 32,768 problem, years after 32,767 may be interpreted as negative numbers, [5] [87] beginning with −32,768 which may be displayed as 32,768 BC.
The 16-bit word length thus became more common in the 1960s, especially on minicomputer systems. Early 16-bit computers (c. 1965–70) include the IBM 1130, [3] the HP 2100, [4] the Data General Nova, [5] and the DEC PDP-11. [6] Early 16-bit microprocessors, often modeled on one of the mini platforms, began to appear in the 1970s.