Binary to Decimal to Hexadecimal Converter

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Decimal, Binary, and Hexadecimal Systems

Decimal System (Base 10) The decimal numeral system is the standard system for denoting integer and non-integer numbers. It uses 10 digits from 0 to 9. Each digit's position represents a power of 10. For example, in the number 123, the digit 3 is in the ones place (10^0), the digit 2 is in the tens place (10^1), and the digit 1 is in the hundreds place (10^2).

Binary System (Base 2) The binary numeral system uses only two digits: 0 and 1. It is commonly used in computing because it is easy to implement with digital electronics. Each digit's position represents a power of 2. For example, in the binary number 101, the digit 1 is in the ones place (2^0), the digit 0 is in the twos place (2^1), and the digit 1 is in the fours place (2^2).

Hexadecimal System (Base 16): The hexadecimal numeral system uses 16 digits: 0-9 and A-F (representing values 10-15). It is widely used in computing, especially in representing memory addresses, colors, and other data. Each digit's position represents a power of 16. For example, in the hexadecimal number 1A3, the digit 3 is in the ones place (16^0), the digit A is in the sixteens place (16^1), and the digit 1 is in the 256s place (16^2).

How to Convert Numbers

Binary to Decimal Conversion

To convert a binary number to decimal:

• Start from the rightmost digit.
• Multiply each digit by 2 raised to the power of its position (starting from 0).
• Add up all the results to get the decimal equivalent.

Example: 1011₂ to decimal:

1 × 20 + 1 × 21 + 0 × 22 + 1 × 23 = 1110

Decimal to Binary Conversion

To convert a decimal number to binary:

• Divide the decimal number by 2 repeatedly, keeping track of the remainders.
• The remainders, read from bottom to top, give the binary equivalent.

Example: 25₁₀ to binary:

25 ÷ 2 = 12 (remainder 1)
12 ÷ 2 = 6 (remainder 0)
6 ÷ 2 = 3 (remainder 0)
3 ÷ 2 = 1 (remainder 1)
1 ÷ 2 = 0 (remainder 1)


So, 2510 = 110012

Decimal to Hexadecimal Conversion

To convert a decimal number to hexadecimal:

• Divide the decimal number by 16 repeatedly, keeping track of the remainders.
• The remainders, read from bottom to top, give the hexadecimal equivalent.

Example: 201₁₀ to hexadecimal:

201 ÷ 16 = 12 (remainder 9, which is represented as 916)
12 ÷ 16 = 0 (remainder 12, which is represented as C16)

So, 20110 = C916

Hexadecimal to Decimal Conversion

To convert a hexadecimal number to decimal:

• Start from the rightmost digit.
• Multiply each digit (in decimal representation) by 16 raised to the power of its position (starting from 0).
• Add up all the results to get the decimal equivalent.

Example: C9₁₆ to decimal:

9 × 160 + 12 × 161 = 20110
Note, C₁₆ = 12₁₀.

Hexadecimal to Binary Conversion

To convert a hexadecimal number to binary:

• Create a table, similar to the one listed above, that maps each hexadecimal digit (0-9, A-F) to its 4-bit binary representation.
• Replace each hexadecimal digit with its 4-bit binary representation.

Example: C9₁₆ to binary:

C16 corresponds to 11002
916 corresponds to 10012

So, C916 = 110010012