Convert the hexadecimal number (1E2)16 to decimal.
Understand the Problem
The question is asking to convert a hexadecimal number into its decimal equivalent. The high-level approach involves understanding the place values in hexadecimal and calculating the decimal value accordingly.
Answer
419
Answer for screen readers
The decimal equivalent of the hexadecimal number is 419.
Steps to Solve
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Identify the Hexadecimal Digits Start by identifying the digits in the hexadecimal number. For example, in the number "1A3", the digits are 1, A, and 3.
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Convert Hexadecimal Digits to Decimal Values Convert each hexadecimal digit to its decimal equivalent. In hexadecimal:
- 1 is 1
- A is 10
- 3 is 3
- Determine Place Values Each digit in the hexadecimal number has a place value based on its position, starting from the right (0 index):
- The rightmost digit (3) is multiplied by $16^0$.
- The next digit (A) is multiplied by $16^1$.
- The leftmost digit (1) is multiplied by $16^2$.
- Calculate Each Value Calculate the decimal values for each digit:
- For 3: $3 \times 16^0 = 3 \times 1 = 3$
- For A: $10 \times 16^1 = 10 \times 16 = 160$
- For 1: $1 \times 16^2 = 1 \times 256 = 256$
- Sum the Values Add all the values obtained from the calculations: $$ 3 + 160 + 256 = 419 $$
The decimal equivalent of the hexadecimal number is 419.
More Information
Hexadecimal is a base-16 number system, which means it uses 16 symbols: 0-9 for values zero to nine and A-F for values ten to fifteen. This system is commonly used in computing and digital systems because it is more compact than binary.
Tips
- Confusing hexadecimal digits (like A, B, etc.) with their decimal values. Remember that A=10, B=11, C=12, D=13, E=14, F=15.
- Forgetting to multiply each digit by the correct power of 16 based on its position.
