5.1 Introduction to computer organization

Computer architecture

To understand digital signal processing systems, we must understand a little about how computers compute. The moderndefinition of a computer is an electronic device that performs calculations on data, presenting theresults to humans or other computers in a variety of (hopefully useful) ways.

Organization of a simple computer

The generic computer contains input devices (keyboard, mouse, A/D (analog-to-digital) converter, etc.), a computational unit , and output devices (monitors, printers, D/A converters). Thecomputational unit is the computer's heart, and usually consists of a central processing unit (CPU), a memory , and an input/output (I/O) interface. What I/O devices might be present on a givencomputer vary greatly.

• A simple computer operates fundamentally in discrete time. Computers are clocked devices, in which computational steps occur periodically according to ticksof a clock. This description belies clock speed: When you say "I have a 1 GHz computer," you mean that your computertakes 1 nanosecond to perform each step. That is incredibly fast! A "step" does not, unfortunately,necessarily mean a computation like an addition; computers break such computations down into several stages, whichmeans that the clock speed need not express the computational speed. Computational speed is expressed inunits of millions of instructions/second (Mips). Your 1 GHz computer (clock speed) may have a computational speedof 200 Mips.
• Computers perform integer (discrete-valued) computations. Computer calculations can be numeric (obeying the laws of arithmetic), logical (obeyingthe laws of an algebra), or symbolic (obeying any law you like). An example of a symbolic computation is sorting a list of names. Each computer instruction that performs an elementary numeric calculation --- an addition, a multiplication, or adivision --- does so only for integers. The sum or product of two integers is also an integer, but the quotient oftwo integers is likely to not be an integer. How does a computer deal with numbers that have digits to the rightof the decimal point? This problem is addressed by using the so-called floating-point representation of real numbers. At its heart, however, this representation relies on integer-valued computations.

Representing numbers

Focusing on numbers, all numbers can represented by the positional notation system . Alternative number representation systems exist. For example, we could use stick figure counting orRoman numerals. These were useful in ancient times, but very limiting when it comes to arithmetic calculations: ever triedto divide two Roman numerals? The $b$ -ary positional representation system uses the position of digits ranging from0 to $b$ -1 to denote a number. The quantity $b$ is known as the base of the number system. Mathematically, positional systems represent the positiveinteger $n$ as