4. Represent the following as a single precision floating point (IEEE 754) number:a) 85.125b) -4.75

Sure, let's break it down step by step:

a) 85.125

Step 1: Convert the integer part to binary 85 in decimal is 1010101 in binary.

Step 2: Convert the fractional part to binary 0.125 in decimal is 0.001 in binary.

So, 85.125 in binary is 1010101.001

Step 3: Normalize the binary number This gives us 1.010101001 x 2^6

Step 4: Determine the sign, exponent, and mantissa The sign is 0 (since the number is positive), the exponent is 6, and the mantissa is 010101001.

Step 5: Adjust the exponent by adding 127 (for single precision) and convert to binary 6 + 127 = 133, which is 10000101 in binary.

Step 6: Assemble the IEEE 754 representation This gives us 0 10000101 01010100100000000000000

b) -4.75

Step 1: Convert the integer part to binary 4 in decimal is 100 in binary.

Step 2: Convert the fractional part to binary 0.75 in decimal is 0.11 in binary.

So, -4.75 in binary is -100.11

Step 3: Normalize the binary number This gives us -1.0011 x 2^2

Step 4: Determine the sign, exponent, and mantissa The sign is 1 (since the number is negative), the exponent is 2, and the mantissa is 0011.

Step 5: Adjust the exponent by adding 127 (for single precision) and convert to binary 2 + 127 = 129, which is 10000001 in binary.

Step 6: Assemble the IEEE 754 representation This gives us 1 10000001 00110000000000000000000