Question

Given a 12-bit IEEE floating point format with 5 exponent bits:

1. Give the hexadecimal representation for the bit-pattern representing −∞−∞.

2. Give the hexadecimal representation for the bit-patterns representing +0 and -1.

3. Give the decimal value for the floating point number represented by the bit-pattern 0xcb0.

4. Give the decimal value for largest finite positive number which can be represented?

5. Give the decimal value for the non-zero negative floating point number having the smallest magnitude.

6. What are the smallest and largest magnitudes for the ULP?

Recall that for unnormalized numbers the biased exponent is the same as the smallest biased exponent for normalized numbers, effectively 1−bias.

Answer 1

1. Common Name - + ∞

Bit Pattern (Hex) - 7f800000

Decimal Value - Infinity

Common Name - −∞

Bit Pattern (Hex) - ff800000

Decimal Value - -Infinity

2. Common Name - +0

Bit Pattern (Hex) - 00000000

Decimal Value - 0.0

Common Name - -1

Bit Pattern - ffffffffffffffff

3. Bit Pattern - 0xcb0

Binary Number - 00000000000000000000110010110000

Decimal Number - 3248

4. Common Name - maximum normal number

Bit Pattern (Hex) - 7f7ffff

Decimal Value - 3.40282347e+38

5. Common Name - 2

Bit Pattern (Hex) - 40000000 00000000

Decimal Value - 2.0

6. double.eps - the smallest positive floating-point number x such that 1 + x != 1. It equals base^ulp.digits if either base is 2 or rounding is 0; otherwise, it is (base^ulp.digits) / 2.

double.max.exp - the smallest positive power of base that overflows.