Final answer:
To represent -0.75 in IEEE 754 single and double precision formats, one must first convert the number into binary, normalize it, find the biased exponent and significand, and then place them into the correct format with appropriate sign, exponent, and fraction fields.
Step-by-step explanation:
Representing the number -0.75 in IEEE 754 single precision and double precision floating point formats involves several steps. First, we find the binary representation of the magnitude of the number (ignoring the sign), which for 0.75 is 0.11 in binary. Then we normalize this to scientific notation, which becomes 1.1 x 2-1. This gives us the significand (1.1) and the exponent (-1).
For single precision, which is 32 bits wide, the layout is 1 bit for sign, 8 bits for exponent, and 23 bits for the fraction (significand minus the leading 1). The exponent is biased by adding 127 to it, so for -1 the biased exponent is 126. Therefore in binary, the exponent is 01111110. The significand is 1.1, with the leading 1 dropped, and the remaining portion (1) is placed into the fraction field, with zeros following to fill up the 23 bits: 10000000000000000000000. The sign bit for a negative number is 1. Hence, the IEEE 754 single precision representation is 10111111010000000000000000000000.
For double precision, which is 64 bits wide, the layout is 1 bit for sign, 11 bits for exponent, and 52 bits for the fraction (significand minus the leading 1). The exponent is biased by adding 1023, making the biased exponent for -1 equal to 1022. In binary, this is 01111111110. The significand remains the same (1.1), but now we fill the fraction field up to 52 bits with zeros: 1000000000000000000000000000000000000000000000000000. The negative sign bit is again 1. The IEEE 754 double precision representation is 1011111111101000000000000000000000000000000000000000000000000000.