Question

the ieee 754 single-precision floating-point representation makes use of an 8-bits exponent, a 23-bits significand, and 127 as a bias. what is the decimal value of the single precision floating point number denoted by 01010000110101000000000000000000?

Answer 1

The decimal value of the given single precision floating point number in IEEE 754 representation is approximately 1.284916995.

Step-by-step explanation:

The decimal value of the single precision floating point number denoted by 01010000110101000000000000000000 in IEEE 754 representation can be calculated by breaking it down into its components. The first bit represents the sign, with 0 indicating positive and 1 indicating negative. The next 8 bits form the exponent, which is biased by 127. Finally, the remaining 23 bits represent the significand, also known as the mantissa.

To calculate the decimal value, we need to convert the exponent and significand into their decimal equivalents. In this case, the exponent is 01010000, which is equivalent to 80 in decimal. Subtracting the bias of 127 from 80 gives -47.

The significand is 11010100000000000000000. To convert this to decimal, we divide it by 2 raised to the power of 23 (2^23). This gives us a value of approximately 0.6689453125.

Finally, we multiply the sign, exponent, and significand to get the decimal value. In this case, the sign is positive (+1), the exponent is -47, and the significand is 0.6689453125. Multiplying these values gives us a decimal value of approximately 1.284916995.