Find the hexadecimal equivalent of the given binary number.
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Find the hexadecimal equivalent of the given binary number.
Binary Number: 11011001111000110001
Show answer & explanation
Answer: D. 1B3C1 (hex)
To convert binary to hexadecimal, group the binary digits into groups of 4 from right to left, then convert each group to its hex equivalent. The binary 11011001111000110001 groups as 1 1011 0011 1100 0110 0001, which converts to 1 B 3 C 1 in hexadecimal, giving 1B3C1.
Step-by-step Derivation:
Step-by-step conversion:
- Binary: 11011001111000110001
- Group into 4-bit chunks from right to left:
1 | 1011 | 0011 | 1100 | 0110 | 0001 - Convert each group:
- 0001 = 1
- 0110 = 6
- 1100 = C (12)
- 0011 = 3
- 1011 = B (11)
- 1 = 1
- Read from left to right: 1B3C1
- Verification: 1×16⁴ + 11×16³ + 3×16² + 12×16¹ + 1×16⁰ = 65536 + 45056 + 768 + 192 + 1 = 111553 (decimal)
Binary to decimal: 2¹⁹ + 2¹⁸ + 2¹⁶ + 2¹⁵ + 2¹¹ + 2¹⁰ + 2⁹ + 2⁵ + 2⁴ + 2⁰ = 524288 + 262144 + 65536 + 32768 + 2048 + 1024 + 512 + 32 + 16 + 1 = 111553 ✓