Understanding Two's Complement in Computer Science

List the steps to find the two’s complement of a number.

• 1. Start with the binary representation of the number. 2. Invert all the bits (change 0s to 1s and 1s to 0s). 3. Add 1 to the inverted binary number.

• 1. Start with the binary representation of the number. 2. Add 1 to the binary number. 3. Invert all the bits (change 0s to 1s and 1s to 0s).

• 1. Invert all the bits (change 0s to 1s and 1s to 0s). 2. Add 1 to the inverted binary number. 3. Start with the binary representation of the number.

• 1. Add 1 to the binary number. 2. Start with the binary representation of the number. 3. Invert all the bits (change 0s to 1s and 1s to 0s).

Answer explanation

To find the two's complement, start with the binary representation, invert all bits, and then add 1 to the result. This method correctly represents the negative of the original number in binary.

How do you convert a two's complement binary number back to decimal?

• By inverting all bits and adding one to the least significant bit

• By converting it directly to decimal as an unsigned number

• By interpreting the most significant bit as a negative weight and summing all bits

• By reversing the binary digits and converting to decimal

Answer explanation

To convert a two's complement binary number to decimal, interpret the most significant bit as a negative weight. Sum the values of the bits, considering the sign, to get the correct decimal representation.

What is the result of adding 1111 1011 (-5) and 0000 0011 (+3) in Two's Complement?

• 1111 1110 (-2)

• 0000 0000 (0)

• 1111 1100 (-4)

• 0000 0010 (+2)

Answer explanation

Adding 1111 1011 (-5) and 0000 0011 (+3) in Two's Complement gives 1111 1110, which is -2 in decimal. Thus, the correct answer is 1111 1110 (-2).

What is the range of an 8-bit Two's Complement number?

• -128 to 127

• 0 to 255

• -256 to 255

• -127 to 128

Answer explanation

An 8-bit Two's Complement number can represent values from -128 to 127. This is because the highest bit is used for the sign, allowing for 256 total values, split evenly between negative and positive ranges.

Two’s Complement is used for:

• Representing positive numbers

• Representing negative numbers

• Performing logical operations

• Storing floating-point numbers

Answer explanation

Two's Complement is a method for representing negative numbers in binary. It allows for straightforward arithmetic operations and simplifies the representation of both positive and negative integers, making it essential for negative number representation.

For 8-bit Two’s Complement, what is the range of numbers?

• -128 to 127

• 0 to 255

• -256 to 255

• -127 to 128

Answer explanation

In 8-bit Two's Complement, the most significant bit indicates the sign. The range is from -2^(n-1) to 2^(n-1) - 1. For n=8, this gives -128 to 127, making '-128 to 127' the correct choice.

What is the minimum value for 8-bit Two’s Complement?

• -128

• -127

• 0

• -256

Answer explanation

In 8-bit Two's Complement, the range of values is from -128 to 127. The minimum value is -128, represented by the binary 10000000. Therefore, the correct answer is -128.

The maximum value for 8-bit Two’s Complement is:

• 127

• 128

• 255

• 256

Answer explanation

In 8-bit Two's Complement, the range is from -128 to 127. The maximum positive value is 127, which is represented as 01111111 in binary. Therefore, the correct answer is 127.

The leftmost bit (MSB) in Two’s Complement indicates:

• The sign of the number

• The magnitude of the number

• The parity of the number

• The overflow of the number

Answer explanation

In Two's Complement representation, the leftmost bit (MSB) indicates the sign of the number: 0 for positive and 1 for negative. Therefore, the correct answer is 'The sign of the number'.

How do you convert negative numbers in Two’s Complement?

• Invert all bits and add one

• Invert all bits and subtract one

• Add one to the number

• Subtract one from the number

Answer explanation

To convert a negative number in Two's Complement, you invert all bits and add one. This process effectively changes the representation of the negative number to its positive counterpart in binary form.