Your question:

\#1 a) Determine the representation of the following decimal numbers in the IEEE 32-bit format (−10.675)10​ b) Convert the following 32-bit machine number in IEEE 32-bit format to a decimal number. 010000011100100000000000000000002​ c) Using IEEE 754 denormalization process to convert the following floating-point number 0.625×2∧(−126) to a 32-bit IEEE machine number.

Assignment Help Answers with Step-by-Step Explanation:

• The absolute value of -10.675 is 10.675.

• The integer part is 10, which is 1010 in binary.

3. Normalize the binary representation:

• Move the binary point left or right to have a single 1 to the left of the binary point. In this case, we have 1010.1011.

• Sign bit: 1

• Exponent (biased): 10000011

1. Sign Bit: The first bit is 0, which means the number is positive.

2. Exponent: The next 8 bits "10000011" represent the exponent in binary.

Now, we need to calculate the value using the formula:

(-1)^sign bit * 2^(exponent - bias) * 1.fraction

(-1)^0 * 2^4 * 1.01010110000000000000000 (binary)

= 1 * 16 * 1.328125

2. Determine the exponent: The exponent is -126. In IEEE 754, you need to add the bias value to the actual exponent. For single-precision (32-bit) format, the bias is 127. So, the biased exponent is 1 (127 - 126).

3. Determine the fraction: The fraction part of the number is 0.625. To represent it in binary, you can use the method of multiplying by 2 and taking the integer part of the result:

• Sign bit: 0

• Exponent (biased): 1