you need to find the sum of the decimal represented bit value * digit of the bit as radix(2) to the power of. 0010 as integer part is equalent 2 0010 as decimal part equals to 0*2^(-1) + 0*2^(-2) + 1*2^(-3) + 0*2^(-4) equals to 0.125
The key piece of info for calculating the mantissa is that you start with bit[51] and work your way down to bit[0]. bit[51]*2^(-1) + bit[50]*2^(-2) + bit[49]*2^(-3) + .... + bit[0]*2^(-52)
Remember that the typical conversion from binary to decimal is dependent on the bit's index in the binary number. For example, 0101 can be calculated using the following method: (1 * 2^0) + (0 * 2^1) + (1 * 2^2) + (0 * 2^3) = 5. Similarly, we can use this method to calculate the mantissa of any binary number with a decimal. Using the example from the video, .10010011000...0, we use the following method: (1 * 2^(-1)) + (0 * 2^(-2)) + (0 * 2^(-3)) + (1 * 2^(-4)) + (0 * 2^(-5)) + (0 * 2^(-6)) + (1 * 2^(-7)) + (1 * 2^(-8)) = 0.57421875. We can stop after the 8th bit in the decimal because there are no additional 1's that will contribute to our decimal value.
