The16 -bit2` scomplement representation of an integer is1111 1111 1111...
for 2's complement 1 111 1111 1111 0101 →2′scomplement→2′scomplement 1 000 0000 0000 1011
1st bit is same not involved in 2's complement same with 1's complement. since msb bit for sign.
Take one's complement and add 1 we get 11, and as it is negative number we get answer as -11
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The16 -bit2` scomplement representation of an integer is1111 1111 1111...
As it is in 2's complement form we generally extend negative sign bits 1 until 16bit..so here last digits 10101 is actual 2's complement value and 1's before this is the extension of sign bit so, we have to consider 10101 value and it's binary weight is first is sign bit so, it has negative weight(remaining are positive) -2^4+0+2^2+0+2^1=-11
The16 -bit2` scomplement representation of an integer is1111 1111 1111...
16-bit 2's Complement Representation:
The given 16-bit 2's complement representation is 1111 1111 1111 0101. This representation can be converted to its decimal equivalent using the following steps:
Step 1: Determine the Sign Bit
The leftmost bit of the 16-bit representation is the sign bit. In this case, the sign bit is 1, which indicates a negative number.
Step 2: Find the 2's Complement
To convert a negative number from its 2's complement representation to decimal, we need to find its 2's complement by inverting all the bits and adding 1 to the result.
Inverting all the bits:
1111 1111 1111 0101
0000 0000 0000 1010
Adding 1 to the result:
0000 0000 0000 1011
Therefore, the 2's complement of the given representation is 0000 0000 0000 1011.
Step 3: Convert to Decimal
To convert the 2's complement representation to decimal, we need to multiply each bit by its corresponding weight and sum them up.
Since the sign bit is 1 (indicating a negative number), we need to find the decimal value of the 2's complement and add a negative sign to it.
Weighted calculation:
(0 * 2^15) + (0 * 2^14) + ... + (0 * 2^2) + (1 * 2^1) + (1 * 2^0)
Simplifying the calculation:
0 + 0 + ... + 0 + 2 + 1
Calculating the sum:
2 + 1 = 3
Adding the negative sign:
-3
Therefore, the decimal representation of the given 16-bit 2's complement representation is -3.
Step 4: Correct Answer
The correct answer given is -11. However, the calculations above show that the decimal representation of the given 16-bit 2's complement is -3. It appears that there may be an error in the given answer. Please double-check the provided information to ensure accuracy.
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