# Zeros and Ones

## Binary System and Binary Signal

A signal in a digital circuit is a circuit net that transports an output voltage from one device to one or more input connections of other devices. In a digital circuit, signals are constrained to be at one of two voltages, either Vdd or GND. Thus, all data in digital circuits are represented by signals that can be in one of only two states, and all data operations combine two-state data inputs to produce two-state data outputs. Systems that use two-state data are known as binary systems, and a two-state signal is a binary signal. The set of voltage values {Vdd, GND} that define the state of a signal wire in a digital system are commonly represented by the numeric symbols {1, 0}, with '1' representing Vdd and '0' representing GND. Since digital systems can only represent two-state data, and since we have already assigned those states the numeric symbols '0' and '1', it follows that data in digital symbols can be represented by binary (base two) numbers. One signal wire in a digital circuit can carry one binary digit (abbreviated to “bit”) of information; groupings of signal wires can carry multiple bits that can define a binary number. Using bits to represent data in digital systems makes is easy to adopt existing logical and numerical techniques to the study of digital circuits. For example, an AND relationship can be logically described as “true” when all inputs are “true” (i.e., output Y is “true” when inputs “A”, “B”, and “C” are all “true”). If we assign the symbol '1' to “true”, then the AND relationship yields a '1' when the inputs are all '1', concisely demonstrated by the truth table in Fig. 1. Since a '1' represents Vdd and a '0' represents GND, this logical AND truth table can define a logic circuit that outputs a '1' (or Vdd) whenever all inputs are a '1'.

A group of individual digital signals may be thought of as a logical group of signals that define a multi-bit data element. Such a logical grouping of signals is called a bus. Because each signal on a bus can carry a '1' or a '0', busses can carry binary numbers. For example, if a 4-bit bus is used to represent a 4-bit binary number, then the bus can carry a binary number from 0 to 15 (0000 to 1111).

## Representing an Analog Signal in a Digital System with Zeros and Ones

In contrast to digital circuits, analog circuits use signals whose voltage levels are not constrained to two distinct levels, but instead can assume any value between Vdd and GND. Many input devices, particularly those using electronic sensors (e.g., microphones, cameras, thermometers, pressure sensors, motion and proximity detectors, etc.) produce analog voltages at their outputs. In modern electronic devices, it is likely that such signals will be converted to digital signals before they are used within the device. For example, a digital voice-memo recording device uses an analog microphone circuit to convert sound pressure waves into voltage waves on an internal circuit node. A special circuit called an analog-to-digital converter, or ADC, converts that analog voltage to a binary number that can be represented as a bus in a digital circuit. An ADC functions by taking samples of the input analog signal, measuring the magnitude of the input voltage signal (usually with reference to GND), and assigning a binary number to the measured magnitude. Once an analog signal has been converted to a binary number, a bus can carry that digital information around a circuit. In a similar manner, digital signals can be reconstituted into analog signals using a digital-to-analog converter. Thus, a binary number that represents a sample of an audio waveform can be converted to an analog signal that can, for example, drive a speaker.

## Noise of a Digital Signal

Analog signals are sensitive to noise sources and loss of signal strength over time and distance, but digital signals are relatively insensitive to noise and loss of strength. This is because a digital signal has two wide voltage bands that define a '0' and '1', and any voltage inside a band is an acceptable encoding. In Fig. 2, a digital signal with tens or hundreds of millivolts of noise defines stable 0's and 1's despite the noise; if this same amount of signal noise were present on an analog signal, the circuit could not possibly function correctly. It is because digital signals are more robust and easier to work with that electronic industries the world over have “gone digital”.

## Important Ideas

• Systems that use two-state data are known as Binary systems, and the signals that represent those two-states of data are called Binary signals.
• One signal in a circuit can carry one binary number; this signal is called a bit.
• Many electronic devices still use analog circuits that are then converted in an analog-to-digital converter (ADC) and then the digital signal is used within the device.
• Compared with Analog signals, Digital signals are relatively insensitive to noise and loss of strength.