Computers operate using the base-2 number system, also known as the binary number system. Digital electronics uses two voltage levels to represent one of two possible numbers or states in a device called a logic gate. Sometime in the description of these states they are represented in simple Boolean logic functions; "true" or "false" conditions, or they can be represented using a "on" or "off" state and of course in a binary form using a "0" or a "1". In a gate; if the voltage level is near 0 volts, it represents a "false", "off" or "0". If the voltage level is near the supply voltage normally 5 volts, sometime 3.3 volts it represents a "true", "on" or a "1". If we call a 0 or 1 state of a logic gate a bit, and string together 8 of these gates, we refer to that as a byte. Four bits of a byte is called a nibble; there are upper and lower nibbles. Digital electronics devices are usually made from large assemblies of logic gates. The easiest way to understand bits is to compare them to something you know: digits. A digit is a single place that can hold numerical values between 0 and 9. Digits are normally combined together in groups to create larger numbers. For example, 5,248 has four digits. It is understood that in the number 5,248, the 8 is filling the "1s place," while the 4 is filling the 10s place, the 2 is filling the 100s place and the 5 is filling the 1,000s place. So you could express things this way if you wanted to be explicit: (5 * 1000) + (2 * 100) + (4 * 10) + (8 * 1) = 5000 + 200 + 40 + 8 = 5248.
Another way to express it would be to use powers of 10. Assuming that we are going to represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written as "10^2"), another way to express it is like this: (5 * 10^3) + (2 * 10^2) + (4 * 10^1) + (8 * 10^0) = 5000 + 200 + 40 + 8 = 5248. Using this scheme we can use the base 2 number system to represent numbers and words. To represent 5248 in binary it would look like the following: (1*2^12) + (0*2^11) + (1*2^10) + (0*2^9) + (0*2^8) + (1*2^7) + (0*2^6) + (0*2^5) + (0*2^4) + (0*2^3) + (0*2^2) + (0*2^1) + (0*2^0) = 4096 + 0 + 1024 + 0 + 0 + 128 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 1010010000000. This technique is the backbone of all our digital products. More will be discussed later on this subject.
In essence digital electronics is as widely interesting as analog electronics. The hardware used in digital electronics is constantly evolving; processors are executing bytes faster and faster, applications and programs are getting more complex and sophisticated, memory chips or modules are becoming larger, cheaper and faster. Devices are becoming smaller and more compact which interface with signals from an analog world. For example, light, temperature, sound, electrical conductivity, electric and magnetic fields are analog. Most useful digital systems must translate from continuous analog signals to discrete digital signals. One advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation due to noise. For example, a continuous audio signal, transmitted as a sequence of 1s and 0s, can be reconstructed without error provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s. An hour of music can be stored on a compact disc as about 6 billion binary bits. In regard to analog signal sampling; a more precise representation of a signal can be obtained by using more binary bits to represent it. On the contrary, in an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain. The Nyquist-Shannon sampling theorem provides an important guideline as to how much digital data is needed to accurately portray a given analog signal. Digital memory and transmission systems can use techniques such as error detection and correction to correct any errors in transmission and storage. In some systems, if a single piece of digital data is lost or misinterpreted, the meaning of large blocks of related data can completely change. There is much more to learn about digital electronics which will be presented in the coming lessons. |