Encode into floating point format:

-
3
3
4

Question

Encode into floating point format:

-
3
3
4

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
Floating‑point encoding commonly uses normalized scientific notation: a sign, a mantissa (or significand) with one nonzero digit to the left of the decimal point (for base 10 this is 1 ≤ |mantissa| < 10), and an exponent giving the power of 10. For a negative integer, the sign is negative and the magnitude is converted into normalized form.

2. Complete reasoning process step by step
Start with the given digits: a negative sign and the digits 3, 3, 4 → the number is −334. To convert to normalized decimal floating‑point form, place the decimal point after the first nonzero digit and count how many places you moved it.

3. Intermediate calculation steps
- Original integer: −334 (which is −334.0)
- Place decimal after first digit: 3.34
- How many places moved? The decimal moved from the end of "334.0" (i.e., after the 4) to after the first digit 3: that is 2 places to the left.
- That movement corresponds to multiplying by 10^2 to recover the original magnitude.
- Combine sign, mantissa, and exponent: −3.34 × 10^2

Check: −3.34 × 10^2 = −3.34 × 100 = −334, so the conversion is exact.

4. Why the correct answer is correct
The representation −3.34 × 10^2 is normalized (mantissa magnitude between 1 and 10) and reproduces the original numeric value when multiplied by 10^2. The negative sign correctly indicates the original negative number.

5. Other options (if multiple choice)
No alternative choices are provided here. Common incorrect forms would be unnormalized versions like −33.4 × 10^1 or −334 × 10^0; although numerically equivalent, they are not normalized (mantissa not in [1,10)). Another wrong form would be wrong exponent or misplaced decimal which would change the value.

6. Conclusion / final confirmation
The normalized floating‑point encoding is −3.34 × 10^2, which matches the provided answer.

Encode into floating point format: - 3 3 4简答题

类似问题

Decode the following bit pattern using the floating-point format discussed in class (answer must be in decimal form): 11101110

Which representation is commonly used for numbers with fractional parts?

Consider the IEEE single-precision floating-point format. Further, consider the case: Exponent bit field = all 1's Fraction bit field not all 0's Then the 'number' represented is NaN (Not a Number) .

Question 30 Choose a, b, c or d as the best answer. The author’s main argument is that the 100:80:100 model __________.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单