Hexadecimal to Decimal Calculator:
The hexadecimal number system, also known as base-16, is widely used in computing and digital electronics. Unlike the decimal system (base-10) which uses digits from 0 to 9, the hexadecimal system includes digits from 0 to 9 and letters from A to F, where:
Hexadecimal is a base-16 number system often used in computer memory addresses, color codes in web design, and programming. It's a compact way to represent binary data.
Computers may work with hexadecimal values internally, but humans typically understand numbers in the decimal system. So converting between them helps bridge this gap for programmers, students, and engineers.
To convert a hexadecimal number to decimal, multiply each digit by 16 raised to the power of its position (starting from right to left, beginning at 0).
Decimal = \((D_n \times 16^n) + (D_{n-1} \times 16^{n-1}) + ... + (D_0 \times 16^0)\)
2F to Decimal
Step 1: Break the hexadecimal number into digits: 2 and F
Step 2: Convert F to decimal \(\rightarrow\) F = 15
Step 3: Apply the formula:
= (2 \times 16^1) + (15 \times 16^0) = (2 \times 16) + (15 \times 1) = 32 + 15 = 47
Answer: 2F in hexadecimal = 47 in decimal.
1A3 to Decimal
Step 1: Break the digits \(\\rightarrow\) 1, A, 3 (A = 10)
Step 2: Apply the formula:
= \((1 \times 16^2) + (10 \times 16^2) + (3 \times 16^0)\) = \((1 \times 256) + (10 \times 16) + (3 \times 1)\) = \(256 + 160 + 3 = 419\)
Answer: 1A3 in hexadecimal = 419 in decimal.
Hexadecimal fractions use negative powers of 16, like so:
Example: Convert 0.A2 (hex) to decimal: = \((10 \times 16^{-1}) + (2 \times 16^{-2})\) = \((10 \times 0.0625) + (2 \times 0.00390625)\) =\( 0.625 + 0.0078125 = 0.6328125\)
Answer: 0.A2 (hex) = 0.6328125 (decimal)
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