Understanding the Base or Radix of a Number System: Converting 11011.011 to Decimal

Introduction: When dealing with number systems, it is crucial to understand the base or radix to accurately convert between systems. This article will delve into the process of converting the binary number 11011.011 to its decimal equivalent, explaining the concept of radix and the steps involved in the conversion.

What is Radix?

Radix, or base, refers to the number of unique digits, including zero, used in a number system. For example, the decimal number system has a base of 10, using the digits 0 through 9. It is important to specify the radix when working with numbers in different systems, as the same sequence of digits can represent different values depending on the base.

Converting Binary to Decimal: The Number System in Question

The binary number 11011.011 is in base 2. Each position in this binary number represents a power of 2, starting from the rightmost digit, which is 2 to the power of 0.

Breaking Down the Integer Part

The integer part of the binary number 11011 can be broken down as follows: 1 * 2^4 16 1 * 2^3 8 0 * 2^2 0 1 * 2^1 2 1 * 2^0 1 Adding these values gives us:

16 8 0 2 1 27.

Breaking Down the Fractional Part

The fractional part 0.011 can be broken down as follows: 0 * 2^{-1} 0 1 * 2^{-2} 0.25 1 * 2^{-3} 0.125 Adding these values gives us:

0 0.25 0.125 0.375.

Combining Both Parts for the Final Decimal Value

When combining the integer and fractional parts, we get the decimal equivalent of 11011.011_2 as follows:

Total 27 0.375 27.375.

Conclusion

Therefore, the base or radix of the number system for the binary number 11011.011 is 2. This example demonstrates the importance of specifying and understanding the radix when dealing with number systems, especially when converting to the decimal system.

Additional Notes

It is important to note that the same sequence of digits can represent different values depending on the base. For instance, 11011.011 can also be a number in other bases (such as 3, 10, 13, or 16) but the conversion process and the resulting value will differ. Therefore, it is crucial to specify the radix when working with numbers in different systems.