Write binary representation of the following hexadecimal numbers. (i) 4026 (ii) BCA1 (iii) 98E (iv) 132.45
Question
Write binary representation of the following hexadecimal numbers.
(i) 4026
(ii) BCA1
(iii) 98E
(iv) 132.45
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Answer
To convert hexadecimal numbers to binary, each hexadecimal digit is substituted with its 4-bit binary equivalent. Let's convert the given hexadecimal numbers to binary:
Conversion Table:
| Hexadecimal Symbol | Binary Equivalent |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| A | 1010 |
| B | 1011 |
| C | 1100 |
| D | 1101 |
| E | 1110 |
| F | 1111 |
(i) 4026
| Hexadecimal Digit | Binary Representation |
|---|---|
| 4 | 0100 |
| 0 | 0000 |
| 2 | 0010 |
| 6 | 0110 |
Binary Representation of 4026: 0100 0000 0010 0110
(ii) BCA1
| Hexadecimal Digit | Binary Representation |
|---|---|
| B | 1011 |
| C | 1100 |
| A | 1010 |
| 1 | 0001 |
Binary Representation of BCA1: 1011 1100 1010 0001
(iii) 98E
| Hexadecimal Digit | Binary Representation |
|---|---|
| 9 | 1001 |
| 8 | 1000 |
| E | 1110 |
Binary Representation of 98E: 1001 1000 1110
(iv) 132.45
For the fractional part, each hexadecimal place value is treated separately before and after the point:
| Hexadecimal Digit | Binary Representation |
|---|---|
| 1 | 0001 |
| 3 | 0011 |
| 2 | 0010 |
| . | . |
| 4 | 0100 |
| 5 | 0101 |
Binary Representation of 132.45: 0001 0011 0010.0100 0101
Summary
4026 (Hex) = 0100 0000 0010 0110 (Binary)
BCA1 (Hex) = 1011 1100 1010 0001 (Binary)
98E (Hex) = 1001 1000 1110 (Binary)
132.45 (Hex) = 0001 0011 0010.0100 0101 (Binary)
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