# Introduction to Binary Number Systems

## Binary Numbers

In electronics, **binary numbers** is the flow of information in the form of zeros and ones used by digital computers and systems. Unlike a linear, or analogue circuits, such as AC amplifiers, which process signals that are constantly changing from one value to another, for example amplitude or frequency, digital circuits process signals that contain just two voltage levels or states, labelled, Logic “0” and Logic “1”.

Generally, a logic “1” represents a higher voltage, such as 5 volts, which is commonly referred to as a HIGH value, while a logic “0” represents a low voltage, such as 0 volts or ground, and is commonly referred to as a LOW value. These two discrete voltage levels representing the digital values of “1’s” (one’s) and “0’s” (zero’s) are commonly called: **BI**nary digi**TS**, and in digital and computational circuits and applications they are normally referred to as binary **BITS**.

### Binary Bits of Zeros and Ones

Because there are only two valid Boolean values for representing either a logic “1” or a logic “0”, makes the system of using **Binary Numbers** ideal for use in digital or electronic circuits and systems.

The *binary number system* is a Base-2 numbering system which follows the same set of rules in mathematics as the commonly used decimal or base-10 number system. So instead of powers of ten, ( **10 ^{n}** ) for example: 1, 10, 100, 1000 etc, binary numbers use powers of two, (

**2**) effectively doubling the value of each successive bit as it goes, for example: 1, 2, 4, 8, 16, 32 etc.

^{n}The voltages used to represent a digital circuit can be of any value, but generally in digital and computer systems they are kept well below 10 volts. In digital systems theses voltages are called “logic levels” and ideally one voltage level represents a “HIGH” state, while another different and lower voltage level represents a “LOW” state.

Digital waveforms or signals consist of discrete or distinctive voltage levels that are changing back and forth 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.

- • Analogue Circuits – Analogue or Linear circuits amplify or respond to continuously varying voltage levels that can alternate between a positive and negative value over a period of time.
- • Digital Circuits – Digital circuits produce or respond too two distinct positive or negative voltage levels representing either a logic level “1” or a logic level “0”.