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Binary to Hex Converter



Converting a Binary Number to Hexadecimal

Binary and hexadecimal are both numeral systems used extensively in computing. The binary system (base-2) uses only two digits: 0 and 1, while the hexadecimal system (base-16) uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. Hexadecimal numbers provide a more compact way to represent binary values, which is particularly useful in programming and digital electronics.

To convert a binary number to its hexadecimal equivalent, the binary number is first grouped into sets of four bits, starting from the right. Each group of four bits is then converted to its corresponding hexadecimal digit. If the number of bits is not a multiple of four, you can add leading zeros to the leftmost group to make it four bits long.

For example, the binary number 11011010 can be converted to hexadecimal by following these steps:

1101 1010

The first group, 1101, is equivalent to D in hexadecimal, and the second group, 1010, is equivalent to A in hexadecimal. Therefore, the hexadecimal equivalent of 11011010 is DA.

Examples

Let’s explore some examples to understand how to convert binary numbers to their hexadecimal equivalents.

1. Convert the binary number 11011010 to hexadecimal.

Answer

First, we identify the given number:

Given:

  • Binary: 11011010

Next, we group the binary digits into sets of four, starting from the right:

Steps:

  • 1101 1010

We then convert each group to its corresponding hexadecimal digit:

  • 1101 = D
  • 1010 = A

The final hexadecimal value is formed by concatenating these digits:

Hexadecimal Equivalent:

DA

Result:

∴ The hexadecimal equivalent of the binary number 11011010 is DA.

2. Convert the binary number 101011 to hexadecimal.

Answer

We start by identifying the number:

Given:

  • Binary: 101011

Next, we group the binary digits into sets of four, starting from the right. Since the number of digits is not a multiple of four, we add a leading zero to the left:

Steps:

  • 0010 1011

We then convert each group to its corresponding hexadecimal digit:

  • 0010 = 2
  • 1011 = B

The final hexadecimal value is formed by concatenating these digits:

Hexadecimal Equivalent:

2B

Result:

∴ The hexadecimal equivalent of the binary number 101011 is 2B.

3. Determine the hexadecimal equivalent of the binary number 11111111.

Answer

First, we identify the given number:

Given:

  • Binary: 11111111

Next, we group the binary digits into sets of four, starting from the right:

Steps:

  • 1111 1111

We then convert each group to its corresponding hexadecimal digit:

  • 1111 = F
  • 1111 = F

The final hexadecimal value is formed by concatenating these digits:

Hexadecimal Equivalent:

FF

Result:

∴ The hexadecimal equivalent of the binary number 11111111 is FF.

4. Convert the binary number 1001 to hexadecimal.

Answer

We start by identifying the number:

Given:

  • Binary: 1001

Since this binary number already has four digits, we can convert it directly:

Steps:

  • 1001 = 9

The final hexadecimal value is:

Hexadecimal Equivalent:

9

Result:

∴ The hexadecimal equivalent of the binary number 1001 is 9.