Find the signed binary expansion of the number -6.
Find the signed binary expansion of the number -6.
Show Hint
To convert a negative number into its signed binary representation using two’s complement:
- Write the binary of the positive number.
- Invert the bits and add 1.
10110
11010
11100
10101
The Correct Option is B
Solution and Explanation
Step 1: Understanding Signed Binary Representation
In signed binary representation, negative numbers are represented in two’s complement form.
The two’s complement representation uses the most significant bit (MSB) to indicate the sign of the number, where ‘0’ represents positive and ‘1’ represents negative numbers.
Step 2: Find Binary Expansion for 6
The binary representation of +6 is 0110 in 4-bit binary.
Step 3: Apply Two’s Complement to Get -6
To convert 6 to -6, we perform the following steps:
- Invert all the bits of
0110→1001 - Add 1 to the result:
1001 + 1 = 1010Thus, the two’s complement representation of -6 in 4-bit is1010.
Step 4: Extending to 5 Bits for Signed Expansion
To extend this to 5 bits, we need to add an additional '1' at the left for the negative sign, resulting in 11010.
Thus, the correct answer is (B).
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