Question

Consider the following 32 bit binary representation of the value using IEEE 754 single precision floating point representation. Show the corresponding signed number in decimal.

01000001001010100000000000000000

Answer 1

Here I am providing the answer to your question along with the explanation.

point Converting IEEE 754 32-bit floating notation to its decimal equivalent - Scientifre Notation Given 32-bit binary number *xxXx X 2e 000 0001 0010 1010 0000 0000 0000 0000 exponent fraction bits bits Sign bit * The sign bit represents whether it is positive or negative. * And the next eight bits are exponent bits. ( 100 00010) = 0x2°+ 1x2 + . ---1x27 a 0+2+ 128 a 130 * Now, we calculate the exponent bics exponent bias & 127 @=130-127 * Now we calculate the mantissa we are going to do it multiply each bit by a certain number.

m=0x2 + 1x2 2 + 0x 23 +1x24+.. + 1x26 + = 2^2+244 +26 e => 0.328125 Now putting in General form we get, (-1) Cortm) x 20 sa sign of the binary ma mantissa e= exponent substituting the values (-)ºx (140-328125) x 2° 1 X 1.328125 X 23 = 10-625