Question

Calculate 3.41796875 *10-3 by hand, assuming each of the values are stored in the 16-bit half precision format

Show work and explain

Answer 1

The decimal number is 3.41796875 *10^-3

3.41796875 *10^-3 = 0.00341796875

Since number is positive sign = 0

(0.00341796875)₁₀ = (0.00000000111)₂.

The binary number is 0.00000000111

It is also written as 1.11 * 2^-9

Mantissa = 11

^{Exponent = 1 (Since 2 power value is -9)}

IEEE Exponent = Exponent + Bias

Here Bias is 15 (Since IEEE 16-bit).

IEEE Exponent = -9 + 15 = 6

IEEE Exponent _(Binary) = 110

IEEE 754 format 16 - bit half precision format:

sign	IEEE Exponent	Mantissa
0	00110	1100000000