Digital electronics binary number system

In a digital measurement, the number of pulses occurring within a specified set of boundary conditions is counted. The easiest way to count is to have the pulses represented as binary numbers. In this way, only two electronic states are required. To represent the decimal numbers from 0 to 9, one would need 10 different states. Typically, the binary numbers 0 and 1 are represented electronically by voltage signals of 0.5 and 5 V, respectively. Binary numbers characterize coefficients of the power of 2, so that any number of the decimal system can be described. 

In binary numbers, instead of counting upwards from 1 to 2, the counting has to jump all the way to 10, since there are no twos available, only zeroes and ones. Then, the third number is 11, and the fourth has to go all the way to 100, and so on. This is the heart of "digital" electronics. (More aspects of digital systems will be explained in later chapters. Simplified examples of digital computation and machine language will be included in the last experiments of this course.)... 

The main difficulty in using the computer for sound synthesis is that it works only with discrete domains and the knowledge of sounds that science has generated throughout history is essentially analog. Moreover, computers fundamentally deal only with binary numbers. In contrast to the decimal numeric system, which uses ten different symbols (i.e. from 0 to 9) to represent numbers, the binary system uses only two symbols 0 and 1. Computers are made of tiny electronic switches, each of which can be in one of two states at a time on or off, represented by the digits T and O, respectively. Consequently, the smallest unit of information that the computer can handle is the bit, a contraction of the term binary digit. For instance, the decimal numbers 0, 1, 2 and 3 are represented in the binary system as 0,1,10 and 11 respectively. 

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