Four variations in the paper's own format. Scratch paper only, 4 minutes each. The answers are on a separate page so nothing is visible while you work.
Method, one line: sign bit · exponent = unsigned field − 127 · value = 1.fraction × 2^exponent, evaluated to a number.
The format for a 32-bit Floating Point number is shown below. Use this to answer the following questions.
| S | Exponent | Fraction | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Q3.1 Floating Point - Sign 0.75
Is the number positive or negative?
Q3.2 Floating Point - Exponent Component 0.75
Accounting for the bias (127), what is the actual value of the exponent?
Q3.3 Floating Point - Fractional Component 0.75
What is the fractional component in decimal?
Q3.4 Extra Credit: Floating Point - Decimal 0 pts, worth 2
Convert the entire number to decimal form.
The format for a 32-bit Floating Point number is shown below. Use this to answer the following questions.
| S | Exponent | Fraction | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Q3.1 Floating Point - Sign 0.75
Is the number positive or negative?
Q3.2 Floating Point - Exponent Component 0.75
Accounting for the bias (127), what is the actual value of the exponent?
Q3.3 Floating Point - Fractional Component 0.75
What is the fractional component in decimal?
Q3.4 Extra Credit: Floating Point - Decimal 0 pts, worth 2
Convert the entire number to decimal form.
The format for a 32-bit Floating Point number is shown below. Use this to answer the following questions.
| S | Exponent | Fraction | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Q3.1 Floating Point - Sign 0.75
Is the number positive or negative?
Q3.2 Floating Point - Exponent Component 0.75
Accounting for the bias (127), what is the actual value of the exponent?
Q3.3 Floating Point - Fractional Component 0.75
What is the fractional component in decimal?
Q3.4 Extra Credit: Floating Point - Decimal 0 pts, worth 2
Convert the entire number to decimal form.
The format for a 32-bit Floating Point number is shown below. Use this to answer the following questions.
| S | Exponent | Fraction | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Q3.1 Floating Point - Sign 0.75
Is the number positive or negative?
Q3.2 Floating Point - Exponent Component 0.75
Accounting for the bias (127), what is the actual value of the exponent?
Q3.3 Floating Point - Fractional Component 0.75
What is the fractional component in decimal?
Q3.4 Extra Credit: Floating Point - Decimal 0 pts, worth 2
Convert the entire number to decimal form.