# Binary Number System / Binary Numbers

A binary number system is a stream of zeros and one-in-one information used by digital computers and systems.

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Unlike linear or analog circuits, such as AC amplifiers, which process signals that continuously change from one value to another, such as amplitude or frequency, digital circuits process signals labeled Logic "0" and Logic "1", containing only two voltage levels or states.

In general, logic "1" represents a higher voltage, such as 5 volts, called HIGH, while logic represents a low voltage such as "0", 0 volts, or earth (GND), and is generally expressed as follows: With low values referred to as 1 from 0, we refer to these two discrete values for use in digital circuits and calculations as "**BITS**", referring to the abbreviations "**BI**nary digi**TS**".

## Binary Bits of Zeros and Ones

Because there are only two valid boolean values to represent Logic "1" or Logic "0", the binary number system is used in digital or electronic circuits and systems.

A binary number system is a Base-2 numbering system that follows the same mathematical rules as the commonly used de deity or 10-based number system. Therefore, instead of ten ( 10n ), for example: binary numbers 1, 10, 100, 100, etc. effectively double the value of each consecutive bit as it progresses, using the powers of two (2n), for example: 1, 2 , 4, 8, 16, 32, etc.

The voltages used to represent a digital circuit can be of any value, but usually in digital and computer systems they are kept well below 10 volts. In digital systems, these voltages are called "logic levels" and ideally one voltage level represents the "HIGH" state, while the other different and lower voltage level represents the "LOW" state. A binary number system uses both of these situations.

Digital waveforms or signals consist of discrete or different voltage levels that alternate between these two "HIGH" and "LOW" states. But what makes a signal or voltage "Digital" and how can we represent these "HIGH" and "LOW" voltage levels. Electronic circuits and systems can be divided into two main categories.

• Analog Circuits – Analog or Linear circuits increase or respond to ever-changing voltage levels, which can vary between positive and negative values over a period of time.

• Digital Circuits – Digital circuits produce or react to two very different levels of positive or negative voltage, representing the logic level "1" or the logic level "0".

## Analog Voltage Output

A simple example of the differences between an analog circuit and a digital circuit is shown below:

This is an analog circuit. The output from the ponsiometer changes when the wiper terminal is rotated and produces an infinite number of output voltage points between 0 volt and VMAX. The output voltage can change slowly or quickly from one value to another, so there is no sudden or gradual change between the two voltage levels, thus producing a continuously variable output voltage. Analog signal samples include temperature, pressure, fluid levels and light intensity.

## Digital Voltage Output

In this example of a digital circuit, the ponciometer wiper has been replaced with a single rotary switch that connects sequentially to each connection of the serial resistance chain, forming a basic network of potential dividers. When the switch is returned to the output voltage after a position (or node), VOUT changes rapidly at separate and different voltage levels, representing multiples of 1.0 volts in each switching action or step, as shown in the output graph.

For example, the output voltage will be 2 volts, 3 volts, 5 volts, etc., but not 2.5V, 3.1V or 4.6V. Better output voltage levels can be easily generated by using a multi-position switch and increasing the number of resistant elements within the potentially divisive network, thereby increasing the number of separate switching steps.

Next, we can see that the biggest difference between an analog signal or quantity and a digital quantity is that an "Analog" quantity constantly changes over time, and a "Digital" quantity has discrete (step-by-step) values. "LOW" to "HIGH" or "HIGH" to "LOW."

A good example of this can be a light dimming setting that changes the light intensity (brightness) in your home up or down when rotated between fully ON (maximum brightness) and completely OFF, producing an ever-changing analog output. On the other hand, with a standard wall-mounted light switch, the light is either "ON" (HIGH) or "OFF" (LOW) when the switch is activated. As a result, there is no difference between producing a kind of ON-OFF digital output.

Some circuits combine both analog and digital signals, such as an analog-to-digital converter (ADC) or a digital-to-analog converter (DAC). In both cases, the digital input or output signal represents a binary number value equivalent to an analog signal.

## Digital Logic Levels

On all electronic and computer circuits, only two levels of logic are allowed to represent a single state. These levels are called logic 1 or logic 0, HIGH or LOW, True or False, ON, or OFF. Most logic systems use positive logic; in this case a logic "0" is represented by zero volts, and a logic of "1" is represented by a higher voltage. For example, as shown, the TTL logic is +5 volts.

In general, the transition of a hand tool from ">0" to "1" or "1" to "0" is made early, when it is possible for the correct key receiver of the circuit. Standard TTL (transistor-transist-logic IC's have input and output limits designed to exactly what you have done with "1" and logic "0", such as virtual.

### TTL Input & Output Voltage Levels

Then, when a supply of +5 volts is used, any voltage input between 2.0v and 5v is recognized as the logic "1" value, and any voltage input below 0.8v is recognized as the logic "0" value.The output of a logic gateway between 2.7v and 5v represents a logic "1" value and a voltage output below 0.4v represents a logic "0".This is called "positive logic" and is used in digital logic trainings.

Then binary numbers are widely used in digital and computer circuits and are represented by logic "0" or logic "1".Binary numbering systems are best suited to digital signal encoding because they use only one digit and two digits, zero, to generate different numbers.In this section on binary numbers, we'll look at how to convert decimal or 10-based numbers to octet numbers, hexadecimal numbers, and binary numbers.

Therefore, in the next lesson about **binary numbers** and binary number system , we will look at converting decathlete numbers to binary numbers, and vice versa, and introduce the concept of **Bytes** and **Words** to represent parts of a much larger binary number.