The output voltage of an aircraft altimeter is to be sampled using an ADC. The sensor outputs 0 V at 0 m altitude and outputs 10 V at $10,000 \mathrm{~m}$ altitude. If the allowable error in sensing ( $\pm \frac{1}{2} \mathrm{LSB}$ ) is 10 m , find the minimum number of bits required for the ADC .