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.

To convert -33.75 into IEEE 754 Single Precision Floating Point representation, follow these steps:

1. Sign Bit: Since the number is negative, the sign bit is 1.

2. Convert to Binary: Convert the absolute value of the number to binary. The integer part, 33, converts to 100001. The fractional part, .75, converts to .11. So, 33.75 in binary is 100001.11.

3. Normalize: Move the binary point to the left of the most significant 1 and count the number of moves. The normalized form is 1.0000111 x 2^5.

4. Exponent: Add 127 to the number of moves (5 in this case) to get the exponent in excess-127 form. 5 + 127 = 132, which is 10000100 in binary.

5. Mantissa: Take the fraction part of the normalized form (0000111) and pad it with zeros on the right to make it 23 bits long. So, the mantissa is 00001110000000000000000.

6. Combine: Combine the sign bit, exponent, and mantissa to get the final IEEE 754 representation: 1 10000100 00001110000000000000000.

As for representing zero in this format, it's quite simple. The sign can be either 0 (for +0) or 1 (for -0), the exponent is all zeros, and the mantissa is also all zeros. So, +0 is represented as 0 00000000 00000000000000000000000 and -0 is represented as 1 00000000 00000000000000000000000.