In: Computer Science
Please convert 2.75 into IEEE-754 format.
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Converting 2.75 to binary Convert decimal part first, then the fractional part > First convert 2 to binary Divide 2 successively by 2 until the quotient is 0 > 2/2 = 1, remainder is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 10 So, 2 of decimal is 10 in binary > Now, Convert 0.75 to binary > Multiply 0.75 with 2. Since 1.5 is >= 1. then add 1 to result > Multiply 0.5 with 2. Since 1.0 is >= 1. then add 1 to result > This is equal to 1, so, stop calculating 0.75 of decimal is .11 in binary so, 2.75 in binary is 10.11 2.75 in simple binary => 10.11 so, 2.75 in normal binary is 10.11 => 1.011 * 2^1 single precision: -------------------- sign bit is 0(+ve) exp bits are (127+1=128) => 10000000 Divide 128 successively by 2 until the quotient is 0 > 128/2 = 64, remainder is 0 > 64/2 = 32, remainder is 0 > 32/2 = 16, remainder is 0 > 16/2 = 8, remainder is 0 > 8/2 = 4, remainder is 0 > 4/2 = 2, remainder is 0 > 2/2 = 1, remainder is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 10000000 So, 128 of decimal is 10000000 in binary frac bits are 01100000000000000000000 so, 2.75 in single-precision format is 0 10000000 01100000000000000000000 in hexadecimal it is 0x40300000