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To determine if a number is a power of two, conceptually we may repeatedly do integer divide by two until the number won't divide by 2 evenly; if the only factor left is 1, the original number was a power of 2. Using bit and logical operators, there is a simple expression which will return true (1) or false (0):
For example, Microsoft's Windows API maintains the programming language definition of WORD as 16 bits, despite the fact that the API may be used on a 32- or 64-bit x86 processor, where the standard word size would be 32 or 64 bits, respectively. Data structures containing such different sized words refer to them as: WORD (16 bits/2 bytes)
If that memory is arranged in a byte-addressable flat address space using 8-bit bytes, then there are 65,536 (2 16) valid addresses, from 0 to 65,535, each denoting an independent 8 bits of memory. If instead it is arranged in a word-addressable flat address space using 32-bit words, then there are 16,384 (2 14 ) valid addresses, from 0 to ...
To create an index from the output of the function, a modulo can be taken to reduce the size of the domain to match the size of the array; however, it is often faster on many processors to restrict the size of the hash table to powers of two sizes and use a bitmask instead. An example of both modulo and masking in C:
The array elements may be aligned— each element begins on a byte or word boundary— or unaligned— elements immediately follow each other with no padding. PL/pgSQL and PostgreSQL's SQL support bit strings as native type. There are two SQL bit types: bit(n) and bit varying(n), where n is a positive integer. [8]
Instead of performing on individual bits, byte-level operators perform on strings of eight bits (known as bytes) at a time. The reason for this is that a byte is normally the smallest unit of addressable memory (i.e. data with a unique memory address). This applies to bitwise operators as well, which means that even though they operate on only ...
If the status-byte from a device is 0x67 and the 5th flag bit indicates data-ready. The mask-byte is 2^5 = 0x20. ANDing the status-byte 0x67 (0110 0111 in binary) with the mask-byte 0x20(0010 0000 in binary) evaluates to 0x20. This means the flag bit is set i.e., the device has data ready.
Depending on the architecture, decimal integers may have fixed sizes (e.g., 7 decimal digits plus a sign fit into a 32-bit word), or may be variable-length (up to some maximum digit size), typically occupying two digits per byte (octet).