a. The IEEE 754 single precision format, also known as float, uses 32 bits to represent a number. The binary representation of the decimal number 63.25 in the single precision format is as follows:
Sign bit (1 bit): 0 (positive number)
Exponent bits (8 bits): 10000100 (132 in decimal)
Fraction bits (23 bits): 01000000000000000000000
Combining these bits together, the binary representation of 63.25 in the IEEE 754 single precision format is:
01000010001000000000000000000000
b. The IEEE 754 double precision format, also known as double, uses 64 bits to represent a number. The binary representation of the decimal number 63.25 in the double precision format is as follows:
Sign bit (1 bit): 0 (positive number)
Exponent bits (11 bits): 10000000010 (1026 in decimal)
Fraction bits (52 bits): 0100000000000000000000000000000000000000000000000000
Combining these bits together, the binary representation of 63.25 in the IEEE 754 double precision format is:
0100000001001000000000000000000000000000000000000000000000000000