Hexadecimal E5 to Decimal Conversion Explained

This solution explains how to convert a hexadecimal number, specifically E5, into its equivalent decimal (base-10) representation. Understanding this conversion is fundamental in computer science and digital electronics.

Understanding Number Systems

Computers use different number systems. The most common ones are:

• Decimal (Base-10): Uses digits 0-9. This is the system we use daily.
• Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

Converting Hexadecimal E5 to Decimal

To convert a hexadecimal number like E5 to decimal, we multiply each digit by the corresponding power of 16 (the base) and sum the results.

The hexadecimal number is E5.

• The rightmost digit (5) is in the $16^0$ (or $16^0 = 1$) place.
• The next digit to the left (E) is in the $16^1$ (or $16^1 = 16$) place.

First, we find the decimal value for the hexadecimal digit 'E'. In hexadecimal, 'E' represents the decimal value 14.

Calculation Steps:

1. Represent the hexadecimal number E5 in expanded form using powers of 16:

   ${E5}_{16} = (E \times 16^1) + (5 \times 16^0)$

2. Substitute the decimal value for E (which is 14):

   ${E5}_{16} = (14 \times 16^1) + (5 \times 16^0)$

3. Calculate the powers of 16:

   $16^1 = 16$

   $16^0 = 1$

4. Perform the multiplication:

   $(14 \times 16) = 224$

   $(5 \times 1) = 5$

5. Add the results together:

   $224 + 5 = 229$

Therefore, the decimal equivalent of the hexadecimal number E5 is 229.

${E5}_{16} = {229}_{10}$