Suppose that a hypothetical binary computer stores floating point numbers in $16-$bit words as shown:

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

$16$

s

exp

mantissa

Bit $1$ is used for the sign of the number, bit $2$ for the sign of the exponent, bits $3-4$ for the magnitude of the exponent, and the remaining twelve bits for the magnitude of the mantissa. What is machine epsilon for this computer?