Construct -33.75 to IEEE 754 Single precision floating point number. Explainhow zero is represented in this format.

Step 1: Identify the sign The number is negative, so the sign bit is 1.

Step 2: Convert the absolute value of the number to binary The absolute value of -33.75 is 33.75. The integer part 33 in binary is 100001. The fractional part 0.75 in binary is 0.11. So, 33.75 in binary is 100001.11.

Step 3: Normalize the binary number Move the binary point 5 places to the left to make the number between 1 and 2. The normalized number is 1.0000111. The exponent is 5.

Step 4: Add the bias to the exponent The bias for single precision IEEE 754 is 127. So, the biased exponent is 5 + 127 = 132. The binary representation of 132 is 10000100.

Step 5: Write out the mantissa The mantissa is the part after the binary point in the normalized number. So, the mantissa is 0000111000...0 (23 bits in total).

Step 6: Put it all together The IEEE 754 representation is therefore: Sign bit: 1 Exponent: 10000100 Mantissa: 0000111000...0 So, -33.75 in IEEE 754 single precision floating point number is 1 10000100 0000111000...0.

Zero in IEEE 754 format is represented as 0 00000000 0000000000...0 where the first 0 is the sign bit, the next 8 zeros are the exponent, and the last 23 zeros are the mantissa. This represents +0. There is also a -0, which has a sign bit of 1.