Understanding Hexadecimal to Decimal Conversion

Hexadecimal (often shortened to "hex") is a base-16 number system. Unlike the decimal system which uses 10 digits (0-9), hexadecimal uses 16 symbols. These are the digits 0 through 9, and the letters A, B, C, D, E, F to represent the values 10 through 15.

To convert a hexadecimal number to its decimal equivalent, we use place values that are powers of 16. Starting from the rightmost digit, the place values are \(16^0\), \(16^1\), \(16^2\), and so on.

Each digit in the hexadecimal number is multiplied by its corresponding place value (a power of 16), and then these results are added together to get the decimal value.

Converting HEX 2A to Decimal

Let's convert the hexadecimal number HEX 2A to its decimal value. The number HEX 2A has two digits:

• The rightmost digit is 'A'.
• The leftmost digit is '2'.

We assign place values starting from the right:

• The digit 'A' is in the \(16^0\) position.
• The digit '2' is in the \(16^1\) position.

Next, we need to know the decimal equivalent of the hexadecimal digit 'A'. In hexadecimal, A represents the decimal value 10.

Now, we multiply each hexadecimal digit's decimal equivalent by its place value and sum the results:

The calculation for HEX 2A to decimal is:

\(\text{Decimal Value} = (\text{Digit at } 16^1 \text{ position} \times 16^1) + (\text{Digit at } 16^0 \text{ position} \times 16^0)\)

Substituting the values:

\(\text{Decimal Value} = (2 \times 16^1) + (\text{A} \times 16^0)\)

Replace the hexadecimal digit 'A' with its decimal value (10):

\(\text{Decimal Value} = (2 \times 16) + (10 \times 1)\)

Perform the multiplication:

\(\text{Decimal Value} = 32 + 10\)

Finally, perform the addition:

\(\text{Decimal Value} = 42\)

So, the decimal value for HEX 2A is 42.

Revision Table: Common Number Systems

Additional Information: Why Hexadecimal is Used

Hexadecimal is widely used in computing and digital electronics. One main reason is that it provides a more compact representation of binary numbers compared to decimal. Every group of 4 binary digits (a nibble) can be perfectly represented by a single hexadecimal digit. This makes it easier for humans to read and write large binary numbers, such as memory addresses or data values, without losing any information.

For example, an 8-bit binary number (a byte) like 11011010 can be represented by two hexadecimal digits. The first four bits (1101) are decimal 13, which is hex D. The last four bits (1010) are decimal 10, which is hex A. So, 11011010 binary is DA in hexadecimal. This is much shorter and easier to handle than its decimal equivalent, which is 218.