Convert binary 0011110000000101 to Hexadecimal

Question

BlackTom AI · Accepted Answer

Group the 16-bit binary into 4-bit nibbles: 0011 1100 0000 0101.

Relevant concepts:
- One hexadecimal digit represents exactly 4 binary bits (a nibble). Converting binary to hex is done by partitioning into 4-bit groups and converting each group to its hex digit.
- Binary-to-hex mapping: 0000=0, 0001=1, 0010=2, 0011=3, 0100=4, 0101=5, 0110=6, 0111=7, 1000=8, 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F.

Step-by-step conversion:
1. Split the binary: 0011 | 1100 | 0000 | 0101.
2. Convert each nibble:
   - 0011 in binary = 0·8 + 0·4 + 1·2 + 1·1 = 2 + 1 = 3 → hex digit "3".
   - 1100 in binary = 1·8 + 1·4 + 0·2 + 0·1 = 8 + 4 = 12 → hex digit "C".
   - 0000 in binary = 0 → hex digit "0".
   - 0101 in binary = 0·8 + 1·4 + 0·2 + 1·1 = 4 + 1 = 5 → hex digit "5".
3. Combine hex digits in the same order: 3 C 0 5 → 3C05.

Intermediate verification (positional hex to decimal):
- 3C05 (hex) = 3×16^3 + C(12)×16^2 + 0×16 + 5
  = 3×4096 + 12×256 + 0 + 5
  = 12288 + 3072 + 5 = 15365 (decimal).
If you convert the original binary directly to decimal you get the same 15365, confirming correctness.

Why the other choices are incorrect:
- 3C06 would require the last nibble 0101 to be 0110 (binary for 6), which it is not.
- 3C0C would require the last two nibbles to be 0000 1100 (or third nibble = C), but the third nibble is 0000, not 1100.
- 3D05 would require the second nibble to be 1101 (D) instead of 1100 (C).
- 3EF2 differs in multiple nibbles and does not match the given binary groups.

Thus the correct hexadecimal representation is 3C05, matching the provided answer.

Convert binary 0011110000000101 to Hexadecimal单项选择题

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