Convert the decimal number 10767 {10} into its hexadecimal equivalent:
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Convert the decimal number $10767_{10}$ into its hexadecimal equivalent:
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Answer: A. 2A0Fh
Converting 10767 to hexadecimal using repeated division by 16 yields 2A0F. The digit 10 is represented as 'A' and 15 as 'F' in hexadecimal notation. Verification: 2×16³ + 10×16² + 0×16¹ + 15×16⁰ = 8192 + 2560 + 0 + 15 = 10767₁₀.
Step-by-step Derivation:
Decimal to hexadecimal conversion using repeated division by 16:
10767 ÷ 16 = 672 remainder 15 (F)
672 ÷ 16 = 42 remainder 0 (0)
42 ÷ 16 = 2 remainder 10 (A)
2 ÷ 16 = 0 remainder 2 (2)
Reading remainders from bottom to top: 2A0Fh
Verification:
2×16³ + 10×16² + 0×16¹ + 15×16⁰
= 2×4096 + 10×256 + 0 + 15
= 8192 + 2560 + 15
= 10767₁₀ ✓