Math Problem Statement

Convert the following binary representations to their hexadecimal

11110010100

Solution

To convert the binary number 1111001010011110010100 to hexadecimal, follow these steps:

Step 1: Group the binary digits in sets of 4, starting from the right. If needed, add leading zeros to the leftmost group.

11110010100becomes000111100101010011110010100 \quad \text{becomes} \quad 0001 \, 1110 \, 0101 \, 0100

Step 2: Convert each 4-bit group to its hexadecimal equivalent.

  • 00010001 in binary is 11 in hexadecimal.
  • 11101110 in binary is EE in hexadecimal.
  • 01010101 in binary is 55 in hexadecimal.
  • 01000100 in binary is 44 in hexadecimal.

Step 3: Combine the hexadecimal digits.

The hexadecimal representation of 1111001010011110010100 is: 1E541E54


Would you like to go over more examples or need any clarifications?

Here are some follow-up questions:

  1. What is the hexadecimal equivalent of 1011011100110110111001?
  2. How do you convert a binary number to decimal?
  3. Can hexadecimal numbers be used in computer memory addresses?
  4. How do you convert a binary fraction to hexadecimal?
  5. What is the difference between binary, octal, and hexadecimal number systems?

Tip: When converting large binary numbers, it helps to group them in sets of four starting from the right. If the leftmost group has fewer than four bits, just add leading zeros.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Binary to Hexadecimal Conversion

Formulas

Group binary digits in sets of 4
Convert each group to its hexadecimal equivalent

Theorems

Positional Number System Theorem

Suitable Grade Level

Grades 6-10