QUESTION 30 What is the hexadecimal value for the below given decimal number?
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QUESTION 30
What is the hexadecimal value for the below given decimal number?
(6789)₁₀
Show answer & explanation
Answer: A. (1A85)₁₆
To convert decimal 6789 to hexadecimal, repeatedly divide by 16 and track remainders. Reading the remainders in reverse order gives 1A85₁₆. We can verify: 1×16³ + 10×16² + 8×16¹ + 5×16⁰ = 4096 + 2560 + 128 + 5 = 6789₁₀.
Step-by-step Derivation:
Conversion of (6789)₁₀ to hexadecimal:
6789 ÷ 16 = 424 remainder 5
424 ÷ 16 = 26 remainder 8
26 ÷ 16 = 1 remainder 10 (A in hex)
1 ÷ 16 = 0 remainder 1
Reading remainders from bottom to top: 1A85₁₆
Verification:
1×16³ = 1×4096 = 4096
A×16² = 10×256 = 2560
8×16¹ = 8×16 = 128
5×16⁰ = 5×1 = 5
Total: 4096 + 2560 + 128 + 5 = 6789 ✓