Title: CSE 351 23au / LS6 Floating Point

Q: A sign-and-magnitude encoding of real numbers that uses normalized scientific binary notation is known as ___
A: Floating point

Q: What are the three components of the normalized scientific binary notation?
A: Sign (S), Mantissa (M), Exponent (E)

Q: When added to the right of the last non-zero digit, ___ can be added infinitely without changing the value of the numeral
A: Trailing zeros

Q: When do trailing zeros have significance?
A: When the number width is important or fixed

Q: How many bits wide is the sign (S) bit?
A: 1 bit wide (0 or 1)

Q: True or false: In the sign bit, 0 indicates negative and 1 indicates positive.
A: False, 0 indicates positive and 1 indicates negative

Q: To shift between the value and encoded binary, the exponent field uses ___
A: Biased notation

Q: Fill in the bias formula:
2 ___ (w - 1) ___ 1
A: 2^(w - 1) -1

Q: Why is biased notation important?
A: It allows us to represent roughly the same number of positive and negative exponents

Q: The significant digits after (i.e., to the right of) the binary point of a floating point number are stored as the ___
A: Mantissa (M)

Q: True or false: Because the Mantissa in a normalized scientific binary number must be of the form 1.bbbb_2... (each b is either a 0 or 1), we assume the presence of the implicit leading 1 (and don’t actually store it in the encoding)
A: True

Q: What happens if the mantissa is longer than the width of the mantissa field itself?
A: Rounding errors

Q: When E is all 0’s but M is non-zero, it is known as ___
A: denormalized

Q: True or false: Denormalized numbers use an implicit leading 0 instead of 1 and a fixed exponent of 1 - bias
A: True

Q: The special case of floating point indicated by 0b1…1 exponent (largest possible exponent) and 0b0…0 mantissa gives us ___
A: +/- infinity

Q: The special case of floating point indicated by 0b1…1 exponent (all 1’s in exponent) and non-zero mantissa gives us ___
A: not-a-number (NaN)

Q: The special case of floating point indicated by 0b0…0 exponent and 0b0…0 mantissa gives us ___
A: +/- 0

Q: When the result/value we are trying to represent is too large, it results in ___. The stored result is ±∞
A: overflow

Q: When the result/value we are trying to represent is too small, it results in ___. The stored result is ±0
A: underflow

Q: When we cannot represent numbers that fall between two neighboring representable numbers, the stored result is determined by ___
A: rounding