# Digital signal binary numbers and computers

A sample is shown in the figure below. The defining characteristic of this type of waveform is that measuring between any two subsequent identical parts of the waveform results in the same value. This value is referred to as the period and it has units of seconds. There is a second method of measuring the periodic waveform and it is directly related to the period. This measurement is called frequency and it has units of cycles per seconds , also referred to as Hertz Hz.

To convert the measurement of time for a period to the measurement of frequency in hertz, simply invert the period. If it takes 0. The last measurement of a periodic waveform is the duty cycle.

The duty cycle represents the percentage of time that a periodic signal is a logic '1'. Somewhere in the middle is where most periodic signals fall. The measurements for the period and the pulse duration are represented with T and t h respectively as shown in the figure below.

No signal is truly digital. A close examination of a digital signal reveals gradual transitions between logic 1 and logic 0 and vice versa. There are many ways to represent a digital signal over a period of time. The figure below represents a single line a single switch with only two possible values, logic 1 and logic 0.

The area between the horizontal hash marks on the rising and falling edges of the signal represent the period where the signal is undefined and in transition. Sometimes, digital lines are grouped together to perform a single function.

This circumstance may be represented with figures such as the one below. Alternatively, these multiple lines can be combined into a more abstract representation such as the one below. Each of these symbols has one or more inputs lines coming in from the left side and one output line exiting from the right. The symbols can be added together to create complex circuits. For example, adding a small circle to an input or an output of a logic symbol is identical to adding an inverter at that input or output.

Logic 1's or logic 0's are sent into the inputs of these symbols, and by definition, a specific logic 1 or logic 0 is expected on the output. The following section describes which symbols have which outputs based on a certain set of inputs.

Now, we need a method to represent how to combine two or more binary signals to produce an output or function. In general, a truth table shows the relationship between columns of inputs and their associated outputs.

For example, the "NOT" gate shown above has one input and one output. Therefore, there is one column of inputs and one column of outputs. For single input, there are exactly two possible states: Therefore, there will be two rows of data for the NOT truth table. That table is shown below. Otherwise the output is always a logic 0. With two inputs and one output, the AND gate's truth table will have two columns for inputs and one column for outputs.

It is shown below. Note that if input A is a logic 0, it doesn't matter what input B is, the output is always 0. Similarly, if input B is 0, A's state does not matter.

These situations are called "don't cares" and are represented by the symbol X. Using don't cares, we can redo the truth table for the AND gate. The OR gate's output is set to logic 1 if either of the inputs are 1. It is 0 ONLY when both inputs are 0. Most of that storing, transferring, and communicating happens with digital electronics.

In electronics, a voltage level or current flow is a way to represent a value. For example, 5V volts or 0. The makers of electronic devices could, of course, assign any meaning that they want to different voltage values. You would end up with 0. This means that when building an electronic device, it is most often desired to have the energy consumption as low as possible and to have a low voltage. Furthermore, electronic signals are not always very steady and can vary because of surrounding influences, like nearby internal circuits for other electronic devices.

This might then lead to voltage levels where it gets difficult to distinguish which value it represents. As a result, we cannot divide the 5V into 10 steps.

The values could be misinterpreted. A computer might suddenly make wrong calculations because of random interference. This example of voltage ranges shows that it is necessary to have a safe range between two voltage levels in order to read the correct value with percent probability. There are additional methods on the software level to verify that data is read correctly, but this is out of the scope of this article. Binary comes from the Latin language and means that something is composed of two things.

Binary electronics are usually called digital electronics.