Design and implementation

Wednesday, May 20, 2009

The way a CPU represents numbers is a design choice that affects the most basic ways in which the device functions. Some early digital computers used an electrical model of the common decimal (base ten) numeral system to represent numbers internally. A few other computers have used more exotic numeral systems like 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.^[6]

Related to number representation is the size and precision of numbers that a CPU can represent. In the case of a binary CPU, a bit refers to one significant place in the numbers a CPU deals with. The number of bits (or numeral places) a CPU uses to represent numbers is often called "word size", "bit width", "data path width", or "integer precision" when dealing with strictly integer numbers (as opposed to floating point). This number differs between architectures, and often within different parts of the very same CPU. For example, an 8-bit CPU deals with a range of numbers that can be represented by eight binary digits (each digit having two possible values), that is, 2⁸ or 256 discrete numbers. In effect, integer size sets a hardware limit on the range of integers the software run by the CPU can utilize.^[7]

Integer range can also affect the number of locations in memory the CPU can address (locate). For example, if a binary CPU uses 32 bits to represent a memory address, and each memory address represents one octet (8 bits), the maximum quantity of memory that CPU can address is 2³² octets, or 4 GiB. This is a very simple view of CPU address space, and many designs use more complex addressing methods like paging in order to locate more memory than their integer range would allow with a flat address space.

Higher levels of integer range require more structures to deal with the additional digits, and therefore more complexity, size, power usage, and general expense. It is not at all uncommon, therefore, to see 4- or 8-bit microcontrollers used in modern applications, even though CPUs with much higher range (such as 16, 32, 64, even 128-bit) are available. The simpler microcontrollers are usually cheaper, use less power, and therefore dissipate less heat, all of which can be major design considerations for electronic devices. However, in higher-end applications, the benefits afforded by the extra range (most often the additional address space) are more significant and often affect design choices. To gain some of the advantages afforded by both lower and higher bit lengths, many CPUs are designed with different bit widths for different portions of the device. For example, the IBM System/370 used a CPU that was primarily 32 bit, but it used 128-bit precision inside its floating point units to facilitate greater accuracy and range in floating point numbers (Amdahl et al. 1964). Many later CPU designs use similar mixed bit width, especially when the processor is meant for general-purpose usage where a reasonable balance of integer and floating point capability is required.