A machine stores floating$-$point number on a $7-$bit binary format. The $1^{st}$ bit is used for the sign of the number, $2^{nd}$ bit is the sign of the exponent, next $2$ bits are used for the magnitude of the exponent, and the rest of the bits are used for the magnitude of the mantissa. What is the largest base$-10$ positive number that can be represented in the binary format?