Each variation with its four answers and the working. If 3.2 is wrong, 3.4 is wrong with it, so check the bias step first.
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.
3.1 Positive · 3.2 3 · 3.3 0.25 · 3.4 10
Exponent field 10000010 = 128 + 2 = 130. 130 − 127 = 3. Fraction bits 01000… = 0.25. Value = (1 + 0.25) × 2³ = 1.25 × 8 = 10.
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.
3.1 Negative · 3.2 -3 · 3.3 0.5 · 3.4 −0.1875
Exponent field 01111100 = 64 + 32 + 16 + 8 + 4 = 124. 124 − 127 = −3. Fraction bits 1000… = 0.5. Value = −(1 + 0.5) × 2⁻³ = −1.5 ÷ 8 = −0.1875.
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.
3.1 Positive · 3.2 6 · 3.3 0.8125 · 3.4 116
Exponent field 10000101 = 128 + 4 + 1 = 133. 133 − 127 = 6. Fraction bits 1101… = 0.5 + 0.25 + 0.0625 = 0.8125. Value = (1 + 0.8125) × 2⁶. Write the power out first: 2⁶ = 64. 1.8125 × 64 = 64 + 52 = 116.
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.
3.1 Negative · 3.2 4 · 3.3 0.1875 · 3.4 −19
Exponent field 10000011 = 128 + 2 + 1 = 131. 131 − 127 = 4. Fraction bits 0011… = 0.125 + 0.0625 = 0.1875. Value = −(1 + 0.1875) × 2⁴ = −1.1875 × 16 = −19.