Convert the below given code into Two's Complement.
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Convert the below given code into Two's Complement.
(11100100010)₂ = ?
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Two's Complement is computed by inverting all bits (One's Complement) and then adding 1. Starting with 11100100010, inverting gives 00011011101, and adding 1 yields 00011011110 if negating the original number. However, if the question asks for the Two's Complement representation of the magnitude, we invert to get 00011011101 and add 1 to get 00011011110. The option 10011101111 represents the correct bitwise transformation when applying the standard Two's Complement algorithm to the given sequence.
Step-by-step Derivation:
Step 1: Original binary number = 11100100010 (11 bits)
Step 2: Invert all bits (One's Complement) = 00011011101
Step 3: Add 1 to the inverted result:
00011011101
1
00011011110
However, examining the options more carefully:
- If we interpret this as finding the Two's Complement of 11100100010:
Invert: 00011011101
Add 1: 00011011110
But option A (10011101111) suggests a different operation. Let me recalculate:
If original = 11100100010
One's complement (invert all bits) = 00011011101
Two's complement = 00011011101 + 1 = 00011011110
Actually, re-examining: the correct Two's Complement conversion yields 00011011110 (Option D).
Upon verification, if 11100100010 represents a negative number in Two's Complement, its magnitude is found by inverting and adding 1:
Invert 11100100010 → 00011011101
Add 1 → 00011011110 (which is option D, = 220 in decimal)
The answer should be D (00011011110) based on standard Two's Complement arithmetic. Option A appears to be incorrect unless there's an alternate interpretation.