Problem 2 A. (Half Precision) The recent revision of the floating-point standard

Question

Problem 2

A. (Half Precision) The recent revision of the floating-point standard added 16-bit floating-
point precision, with the following format:

1. Assuming that half-precision follows the same philosophy as single and double
precision, what should be the bias for this 5-bit exponent in half precision? __________

2. What real decimal number (or symbol) do you expect each of the following
binary bit patterns represent if they are half precision floating point numbers?
i. 0 00000 0000000000 __________________

ii. 0 01111 0000000000 __________________

iii. 1 10000 0000000000 __________________

iv. 1 11111 0000000000 __________________

v. 1 11111 1111111111 __________________

Explanation / Answer

1. 01111 = 15

2.

I) 0 00000 0000000000 = 0

II)0 01111 0000000000 = 1

III) 1 10000 0000000000 = -2

IV)1 11111 0000000000 = -infinity

V)1 11111 1111111111 = -NAN

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