Understanding 2's Complement

The video tutorial explains how signed integer values are represented in binary using 2's complement. It covers the motivation behind 2's complement, the calculation process, and how to negate numbers. The tutorial also discusses properties of 2's complement and how to extend it in memory. This method avoids the issue of duplicate zero values and is the standard for signed integer representation in modern systems.

What is the main issue with using a high-order bit as a sign indicator in binary representation?

• It makes calculations more complex.

• It allows for too many positive numbers.

• It leads to duplicate zero values.

• It requires more bits for representation.

How does 2's complement solve the problem of duplicate zero representations?

• By making the high-order bit negative.

• By using a separate bit for zero.

• By increasing the number of bits.

• By using a different base for calculations.

In 2's complement, what is the value of the highest order bit in a 4-bit system?

• Negative 4

• Positive 4

• Negative 8

• Positive 8

What is the range of values that can be represented in a 4-bit 2's complement system?

• -7 to 7

• -8 to 8

• -7 to 8

• -8 to 7

How do you compute the decimal value of a 2's complement integer?

• By adding all bits as positive values.

• By subtracting the high-order bit value and adding the rest.

• By converting to hexadecimal first.

• By using only the low-order bits.

What is the first step in negating a 2's complement number?

• Convert to decimal.

• Subtract the high-order bit.

• Flip all the bits.

• Add 1 to the number.

What is the process called when extending a 2's complement number to a larger memory space?

• Bit shifting

• Bit expansion

• Memory extension

• Sign extension

Why is there an off-by-one asymmetry in 2's complement representation?

• Because of the high-order bit being negative.

• Due to the addition of extra bits.

• Because of the limited number of bits.

• Due to the use of hexadecimal conversion.

What is a unique property of the low-order bits in 2's complement?

• They are the same for both signed and unsigned integers.

• They are always zero.

• They determine the sign of the number.

• They are always positive.

What is the main advantage of using 2's complement for signed integer representation?

• It uses fewer bits.

• It eliminates duplicate zero values.

• It simplifies arithmetic operations.

• It allows for more positive numbers.