What is IEEE 754?

IEEE 754 in the explanations

• IEEE 754 specifies that dividing a nonzero number by zero returns positive or negative infinity according to the signs.

  Under IEEE 754, what result does the standard specify for d…

• The IEEE 754 default is round half to even: round to the nearest representable value, and on an exact tie choose the one whose last bit is 0 (even).

  Which rounding method does IEEE 754 specify as the default?

• Under IEEE 754, NaN is "not a number," so it compares unequal to everything, including itself: x == x is false (and x != x is true).

  When x is NaN, what does evaluating x == x give in most pro…

Questions that mention IEEE 754 (14)

1. Which three parts make up an IEEE 754 floating-point number?
2. How are the bits of an IEEE 754 single-precision (32-bit) number allocated among sign, exponent and significand?
3. In IEEE 754 double precision (64-bit), how many bits are the exponent and significand?
4. In IEEE 754 single precision, if the stored exponent field is 130, what is the actual exponent (power of two)?
5. What is the effect of not storing the leading 1 of the significand (the hidden bit) in IEEE 754 normalized numbers?
6. What is the hexadecimal bit pattern of decimal 1.0 in IEEE 754 single precision?
7. What is the machine epsilon (the gap between 1 and the next larger representable number) in IEEE 754 single precision?
8. What is the role of IEEE 754 subnormal numbers?
9. Under IEEE 754, what result does the standard specify for dividing a positive number by zero?
10. In IEEE 754 single precision, what do bit patterns with an all-ones exponent field (255) represent?
11. Which correctly describes +0 and −0 in IEEE 754 floating point?
12. Which rounding method does IEEE 754 specify as the default?
13. Up to what value can IEEE 754 single precision represent every integer exactly, starting from 0?
14. When x is NaN, what does evaluating x == x give in most programming languages?

Related terms

Significand NaN Exponent field Machine epsilon Round half to even Arithmetic shift bfloat16 Booth's algorithm Carry-lookahead adder Carry-save adder