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A 32-bit register can store 2 32 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common representations, the range is 0 through 4,294,967,295 (2 32 − 1) for representation as an binary number, and −2,147,483,648 (−2 31) through 2,147,483,647 (2 31 − 1) for representation as two's complement.
But if we regarded 18 as the running total, we need only add 6 to 18 to get 24. So, 18 was, and 24 now is, the running total. In fact, we would not even need to know the sequence at all, but simply add 6 to 18 to get the new running total; as each new number is added, we get a new running total.
An Adler-32 checksum is obtained by calculating two 16-bit checksums A and B and concatenating their bits into a 32-bit integer. A is the sum of all bytes in the stream plus one, and B is the sum of the individual values of A from each step. At the beginning of an Adler-32 run, A is initialized to 1, B to 0.
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
STEbus 8-Bit/16 MHz: 128 Mbit/s: 16 MB/s: 1987 (standardized) C-Bus 16-bit/10 MHz: 160 Mbit/s: 20 MB/s [30] 1982 HP Precision Bus: 184 Mbit/s: 23 MB/s: STD-32 32-bit/8 MHz: 256 Mbit/s: 32 MB/s [31] NESA 32-bit/8 MHz: 256 Mbit/s: 32 MB/s [32] EISA 32-bit/8.33 MHz: 266.56 Mbit/s: 33.32 MB/s: 1988 VME64 32-64bit: 400 Mbit/s: 40 MB/s: 1981 MCA ...
The above implementation requires 32 operations for an evaluation of a 32-bit value, which can potentially take several clock cycles due to branching. It can be " unrolled " into a lookup table which in turn uses trivial hash function for better performance.
The number of bits (the width of the PC) relates to the processor architecture. For instance, a “32-bit” CPU may use 32 bits to be able to address 2 32 units of memory. On some processors, the width of the program counter instead depends on the addressable memory; for example, some AVR microcontrollers have a PC which wraps around after 12 ...
In 1985, the i386, a 32-bit successor to those processors, introducing the IA-32 32-bit version of the x86 architecture, extended the eight 16-bit registers to 32 bits, with "E" added to the beginning of the register name; in IA-32, the memory address of an operand is the sum of one of those eight registers, one of seven of those registers (the ...