Representation of a decimal number

We will take a simple example to represent decimal number in a format clearly showing how the weights and the associated values form the decimal number. The following examples will make it easier for you to understand how the wights and the values are assigned in other number systems.

Example 1: Represent 592 in decimal number system
We also write it as (592)₁₀

Where the subscript 10 indicates that the its a decimal number.

Step 1: For a given number first write down the weights for the decimal number system as shown below

    10²    10¹    10⁰        ← Weights

Here decimal point is not required since fractional part does not exist.

Step 2: Now assign values to the weights starting from right to left such that LSD has the smallest weight and MSD has the greatest weight.


   10²    10¹    10⁰        ← Weights

5

9

2

    ↑                  ↑
MSD             LSD


Step 3: Multiply each value with its corresponding weights as shown below

5x10²

9x10¹

2x10⁰

Step 4: Compute the sum of the products obtained in Step 3 as shown below

   5x10²  + 9x10¹ + 2x10⁰


= 5x100 + 9x10 + 2x1


= 500 + 90 + 2


=(592)₁₀