Math Problem Statement

.2A7F (hexadecimal) (10 Points)

0010101101110111

1010101001111101

0010101001111111

0010111001101111

Solution

To determine which binary sequence corresponds to the hexadecimal value .2A7F, we first convert .2A7F into binary:

Step 1: Convert each hexadecimal digit to binary

Hexadecimal digits and their binary equivalents:

  • 2 = 0010
  • A = 1010
  • 7 = 0111
  • F = 1111

So, .2A7F in binary is:

binary
0010 1010 0111 1111

Step 2: Compare the options

Looking at the given options:

  1. 0010101101110111
  2. 1010101001111101
  3. 0010101001111111 ← This matches 0010101001111111 exactly.
  4. 0010111001101111

Final Answer:

Option 3: 0010101001111111


Do you want a step-by-step breakdown of the conversion? Let me know!

Here are 5 related questions to expand on this concept:

  1. How do you convert a binary number back to hexadecimal?
  2. What is the decimal equivalent of .2A7F?
  3. How do you differentiate between uppercase and lowercase hexadecimal letters during conversion?
  4. Can you explain how hexadecimal simplifies binary representation?
  5. How would you convert a hexadecimal number to octal?

Tip: When converting hexadecimal to binary, remember each hex digit represents 4 binary bits.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Hexadecimal to Binary Conversion

Formulas

Each hexadecimal digit represents 4 binary bits.
Hexadecimal to binary conversion table.

Theorems

Positional Number System Theory

Suitable Grade Level

Grades 8-10