 This time, I'm going to start with a number in our floating point format, and I'm going to convert it back to a decimal number. So the first step is to write out all the bits in their corresponding fields. So I start with a B, which is 1, 0, 1, 1. Next is E, 1, 0, and then 7, and then 0s. So I have no more bits of precision here. I can notice that my number is negative, and I have an exponent that will be less than 1 after I've added my bias. This should give me 127 minus 3, which is 124. So I will have 124 minus 127 for my exponent, which is negative 3, and my mantissa. So I will get 1.111 times 2 to the negative third. I'd like to convert this back to regular binary because I know how to convert that back to a decimal number. So I will move my binary point three places to the left. So 1, 2, 3. You can see 1, 2, 3. You can look at this. This is the 1 half, 1 fourth, 1 eighth, 1 sixteenth, 1 thirty second, and 1 sixty fourth positions. So I could add all of those terms up, or I can try using our division method to convert this back to decimal. I will start with this 1 and divide by 2. It will give me 0.5. We'll move in this 1 and divide this by 2. Let me 0.75, pull down this 1, divide by 2. Half of 0.75 is 0.375, half of 1 is 0.5. Add those together and I will get 0.875. Now I'll pull down this 1, divide this by 2. Now my division is going to get harder. 0.9. So I get 0.9, 3, 7, 5. And I will bring down a first 0. Divide this by 2. This gives me 0.46875. I will bring over this 0. And do one more round of division. Which gets me 0.234375. So this number includes 1 eighth. So it is larger than 0.125. But it does not include any 1 fourths or 1 halfs. So it's slightly less than 0.25. So this is the decimal equivalent of this floating point number.