Final answer:
The IEEE754 single precision representation of 63.25 is option B) 01000010011111100000000000000000. It involves converting the decimal to the IEEE754 format by identifying the sign bit, normalizing the binary equivalent, adjusting the exponent with a bias, and forming the 32-bit representation.
Step-by-step explanation:
The IEEE754 (single precision) representation of the decimal number 63.25 is option B) 01000010011111100000000000000000. IEEE754 single precision format represents floating-point numbers using 32 bits, with 1 bit for the sign, 8 bits for the exponent, and 23 bits for the mantissa. The steps to convert the decimal number to IEEE754 format are as follows:
- Identify the sign bit. Since 63.25 is positive, the sign bit is 0.
- Write the number in binary form which is 111111.01.
- Normalize the binary number to a format that starts with 1., moving the decimal point 6 places to the left, which gives us 1.1111101 and an exponent of 6.
- Adjust the exponent by adding the bias of 127 (6 + 127 = 133), which converts to binary as 10000101.
- The mantissa is made up of the binary number without the leading 1 (11111010000000000000000).
- Combine the sign bit, exponent, and mantissa to form the 32-bit IEEE754 representation: 0 10000101 11111010000000000000000.
Thus, the IEEE754 format for the number 63.25 is B) 01000010011111100000000000000000.