Question

The smallest number that can be represented in 10 bits 2's complement representation is

Answer 1

Answer:

The number should be 1000000000.

Explanation:

In order to find out the smallest number which can be represented in 10 bits in  2's complement representation would be determined as follows:

For 10 bits the number should be 1000000000.

At first, we have to identify the 1's complement of the binary number.

After this, we need to add 1 to this.

In the last step, we need to identify the 2's complement of the binary number i.e. 1000000000.

Hence the solution has been shown.

Answer 2

Answer:

The smallest number that can be represented in 10 bits 2's complement representation is -1000000000

Explanation:

We must write 1 to the most significant bit and all zeros to LSB while writing smallest 2’s complement number.  

We must write 0 to the Most Significant Bit and all 1s to the less significant bit while writing the largest 2’s complement.

In common we can derive formula as,

Smallest: -2^(N-1)

Greatest / largest: 2^(N-1)

To write 10 bit 2’s complement number which is smallest: -2^(10-1) = -2^(9), which can be simply written as -1000000000