linguistic:paraphrasing
Integer range

Every CPU represents numerical values in a specific way. For example, some early digital computers represented numbers as familiar decimal (base 10) numeral system values, and others have employed more unusual representations such as ternary (base three). Nearly all modern CPUs represent numbers in binary form, with each digit being represented by some two-valued physical quantity such as a "high" or "low" voltage.

Related to numeric representation is the size and precision of integer numbers that a CPU can represent. In the case of a binary CPU, this is measured by the number of bits (significant digits of a binary encoded integer) that the CPU can process in one operation, which is commonly called word size, bit width, data path width, integer precision, or integer size. A CPU's integer size determines the range of integer values on which it can directly operate. For example, an 8-bit CPU can directly manipulate integers represented by eight bits, which have a range of 256 (2) discrete integer values.

Integer range can also affect the number of memory locations the CPU can directly address (an address is an integer value representing a specific memory location). For example, if a binary CPU uses 32 bits to represent a memory address then it can directly address 2 memory locations. To circumvent this limitation and for various other reasons, some CPUs use mechanisms (such as bank switching) that allow additional memory to be addressed.

CPUs with larger word sizes require more circuitry and consequently are physically larger, cost more and consume more power (and therefore generate more heat). As a result, smaller 4- or 8-bit microcontrollers are commonly used in modern applications even though CPUs with much larger word sizes (such as 16, 32, 64, even 128-bit) are available. When higher performance is required, however, the benefits of a larger word size (larger data ranges and address spaces) may outweigh the disadvantages. A CPU can have internal data paths shorter than the word size to reduce size and cost. For example, even though the IBM System/360 instruction set architecture was a 32-bit instruction set, the System/360 Model 30 and Model 40 had 8-bit data paths in the arithmetic logical unit, so that a 32-bit add required four cycles, one for each 8 bits of the operands, and, even though the Motorola 68000 series instruction set was a 32-bit instruction set, the Motorola 68000 and Motorola 68010 had 16-bit data paths in the arithmetic logical unit, so that a 32-bit add required two cycles.

To gain some of the advantages afforded by both lower and higher bit lengths, many instruction sets have different bit widths for integer and floating-point data, allowing CPUs implementing that instruction set to have different bit widths for different portions of the device. For example, the IBM System/360 instruction set was primarily 32 bit, but supported 64-bit floating-point values to facilitate greater accuracy and range in floating-point numbers. The System/360 Model 65 had an 8-bit adder for decimal and fixed-point binary arithmetic and a 60-bit adder for floating-point arithmetic. Many later CPU designs use similar mixed bit width, especially when the processor is meant for general-purpose use where a reasonable balance of integer and floating-point capability is required.