In: Computer Science
In representing -1/4 in IEEE 754, the value of the exponent plus bias (127) is
11111101
01111101
10000000
01111111
b) 01111101 Explanation: ------------- -0.25 Converting 0.25 to binary Convert decimal part first, then the fractional part > First convert 0 to binary Divide 0 successively by 2 until the quotient is 0 Read remainders from the bottom to top as So, 0 of decimal is in binary > Now, Convert 0.25000000 to binary > Multiply 0.25000000 with 2. Since 0.50000000 is < 1. then add 0 to result > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result > This is equal to 1, so, stop calculating 0.25 of decimal is .01 in binary so, 0.25 in binary is 00000000.01 -0.25 in simple binary => .01 so, -0.25 in normal binary is .01 => 1. * 2^-2 single precision: -------------------- sign bit is 1(-ve) exponent bits are (127-2=125) => 01111101 Divide 125 successively by 2 until the quotient is 0 > 125/2 = 62, remainder is 1 > 62/2 = 31, remainder is 0 > 31/2 = 15, remainder is 1 > 15/2 = 7, remainder is 1 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1111101 So, 125 of decimal is 1111101 in binary so, 8-bit exponent is 01111101