Convert the hexadecimal number FEDCBA98 into its equivalent binary for...
Hexadecimal FEDCBA98 converts to binary as: F -> 1111, E -> 1110, D -> 1101, C -> 1100, B -> 1011, A -> 1010, 9 -> 1001, 8 -> 1000. So, the binary equivalent is 1111 1110 1100 1101 1011 1010 1001 1000.
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Convert the hexadecimal number FEDCBA98 into its equivalent binary for...
Understanding Hexadecimal to Binary Conversion
Hexadecimal is a base-16 number system that uses the digits 0-9 and letters A-F. To convert a hexadecimal number into binary, each hexadecimal digit corresponds to a 4-bit binary equivalent.
Steps to Convert FEDCBA98
1. Identify Each Hexadecimal Digit:
- F, E, D, C, B, A, 9, 8
2. Convert Each Digit to Binary:
- F = 1111
- E = 1110
- D = 1101
- C = 1100
- B = 1011
- A = 1010
- 9 = 1001
- 8 = 1000
3. Combine the Binary Values:
- Therefore, FEDCBA98 in binary becomes:
1111 1110 1101 1100 1011 1010 1001 1000
Final Result
The complete binary representation of the hexadecimal number FEDCBA98 is:
- 1111 1110 1101 1100 1011 1010 1001 1000
Choosing the Correct Option
Among the options provided:
- a) 1111 1110 1101 1100 1011 1010 1001 1000
- b) 1110 1111 1100 1101 1011 1010 1001 1000
- c) 1111 1110 1100 1101 1011 1010 1001 1000
- d) 1110 1111 1101 1100 1011 1010 1001 1000
The correct answer is option a) because it accurately reflects the binary conversion of the hexadecimal number FEDCBA98.
Conclusion
The binary equivalent of FEDCBA98 is represented accurately in option a), confirming the conversion process.