The binary equivalent of the hexadecimal number ECE5

Question

BlackTom AI · Accepted Answer

Start by recalling the standard conversion: each hexadecimal digit corresponds to exactly four binary bits (a nibble).

- Hex E converts to binary 1110 because E is 14 in decimal, and 14 in binary is 1110. 
- Hex C converts to binary 1100 because C is 12 in decimal, and 12 in binary is 1100. 
- The next hex E again converts to 1110 for the same reason as the first E. 
- Hex 5 converts to binary 0101 because 5 in decimal is 0101 in binary (with four bits).

Putting those nibble results together in order gives: 1110 1100 1110 0101.

Now evaluate each option:

Option a: 1101 1100 1101 101
- This sequence shows 4-bit groups, but the first group 1101 corresponds to hex D, not E. The third group 1101 again corresponds to D, not E, and the fourth group 101 is incomplete for a 4-bit nibble. This option is inconsistent with the required nibble values and spacing.

Option b: 1101 1100 1101 0101
- Here, the first nibble is 1101 (D) instead of 1110 (E). The second nibble 1100 is correct for C, and the last two nibbles 1101 0101 correspond to D5, not E C E 5. Overall, the nibble sequence does not match E C E 5.

Option c: 1110 1100 1110 101
- The first three nibbles (1110, 1100, 1110) look promising, but the final nibble is 0101 needed; here it is only 101, which is a 3-bit group missing a leading 0. This indicates an incomplete or incorrect nibble for the final digit.

Option d: 1110 1100 1110 0101
- This matches exactly the nibble-for-nibble conversion: 1110 (E), 1100 (C), 1110 (E), 0101 (5). The spacing and bit length are correct throughout, aligning perfectly with the hexadecimal input E C E 5.

Overall, the correct binary representation for the hexadecimal number ECE5 is 1110 1100 1110 0101, which is reflected in option d.

The binary equivalent of the hexadecimal number ECE5单项选择题

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