Question

Define excess 2⁽ᵐ⁻¹⁾.

a. It's calculated by subtracting 2^(m-1) from the value; MSB value is 1
b. It's calculated by adding 2⁽ᵐ⁻¹⁾ to the value; MSB value is 1
c. It's calculated by adding 2⁽ᵐ⁻¹⁾ to the value; MSB value is 0
d. It's calculated by subtracting 2⁽ᵐ⁻¹⁾ from the value; MSB value is 0

Answer 1

Excess 2^(m-1) is a method used to represent signed numbers in binary form by adding a bias value of 2^(m-1) to the original value.

Step-by-step explanation:

Excess 2(m-1) is a method used to represent signed numbers in binary form. It involves adding a bias value of 2(m-1) to the original value. The most significant bit (MSB) of the resulting representation is 0. This method is commonly used in computer systems to perform arithmetic operations on signed numbers.

For example, if we have a 4-bit binary number and want to represent the decimal value -3 using excess 2(4-1), we would first calculate the bias as 2(4-1) = 23 = 8. Then, we add this bias to the absolute value of -3, giving us 8 + 3 = 11 in binary. Finally, we represent 11 as a 4-bit binary number, resulting in 1011.