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Example and the Positional Number System

Each symbol of a positional system corresponds to a different value depending on its position within a number. Each symbol within a positional numbers system corresponds to a different value depending upon its location within a number.

The position of each digit within a positional system determines its value. Each position to its right has a higher place. The next position is “thousand”, then the “thousand”, etc. Meanwhile, the number 1x ten millions, 2x one hundred three hundred, 4x teens, and 4x ones is the number 12345.

Decimal Positional Notation

As you can see, the decimal positional system works as follows: Match the number to its positional values in order to use the positional numbers system. An arrow on the right shows that the table expands according to position.



Radix is used to identify the base for positional number systems. Radix can also be used for describing the number digits used in decimal notation systems. Radix uses 10 as its base.

Position in

It shows the position and decimal numbers. The second position is 2. 2. The third position. 3 is the third position.


The third line calculates positional value using radix and multiplying it by the exponential place. must always be =


Position Value

The first row shows the number base, or the radix.

Example – 54321


Binary Positional Note

The binary positional system works in a similar way to the decimal system. As shown in the figure below, it also has a Radix or Position. This is the position of the binary from left to right.




Conversion of Binary and Decimal

It is essential to understand binary numbering by first converting binary numbers from decimal numbers (base-2 to base-10 numbers) and back. It is essential to be able to understand subnetting as well as IP address.


Binary Conversion

Network technicians must be able to convert binary numbers from decimal to binary.

Binary and Decimal with Positional Notation

Positional Notation is a popular way to convert binary data into decimal. A binary number 11000110 can be converted to the decimal system 10 with the positional notation.

Below is an example of how you can convert binary to decimal. Start by writing down the positional number. Then right-click on it to see an example of how to convert binary into decimal.


From right-to-left, the positional values double. The first positional value is 1. The next positional value is 2. This is twice the value 1 (the first place), and the third positional value is 4. This also represents twice the second position value.

10111100 Next, calculate the positional number based on the number digits in your binary number. The decimal equivalent of a binary number is the sum of all the numbers below the line.


You now have an understanding of how to convert binary numbers into decimal. Now we are able to convert a binary IPv4 address to its dotted decimal equivalent. Next, calculate the binary value of the first binary number.

For example, consider that 11110110.10111111.11101011.11011011 is the binary IPv4 address. To convert the binary address into decimal, you will need to start at the first octet of the positional value in row 1. Enter the 8-bit binary value under row 1, and then calculate the decimal number for first octet using the dotted decimal notation. Convert the remainder of the octets. Next, convert the remaining octets to IP addresses using dotted decimal notation.


Decimal To Binary Conversion

Decimal to binary conversion is also possible. A dotted decimal IPv4 can be converted to binary.



As shown in figure below, write down positional value starting at left.


Compare if the remainder (114) is equal to or greater than the next-most-significant bit (64). If the answer is yes, then add binary 1 to the 64 positional values and subtract 64 from the decimal numbers (114-64 =50). If not, enter binary 0 below 64 positional value.


If the answer is yes, then add binary 1 to the 32 positional number and subtract 32 from the decimal value (50 -32 = 18 in our example). If not, enter binary 0 below 64 positional value.


Compare if the remainder (18) is equal to or greater than the next-most-significant bit (16). If the answer is yes, then add binary 1 to the 16 positional values and subtract 16 positional values from the decimal numbers (18 -16 =2). If not, enter binary 0 below 16 positional values.


The reminder (2) can be compared to the next-most relevant bit to show that less than 80 percent of the value remains. Add a binary 0, to each of the 8 positional positions and then move on to the next one. This positional value is not the only one. Add 0 to the positional to move to the next value. Subtract (2) from this positional (2-2=0), then add the 0 to the end.

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