19:05 That's half-right. The complement you've done there is called "1s complement". It's used for representing negative numbers in binary. There are a few problems with it though: 1. With addition you need to do the "end-around carry" thing where you bring the 1st digit over to the end 2. There are two zeros! 000...00 and 111...11. So people have come up with a better way to do it, "2s complement", which is almost the same as 1s complement, except the values of all negative numbers are decremented. This gets rid of the second zero, and it also has more mathematical meaning: it's almost the same as normal binary, except the first digit has a negated place value.
The first method is really a combination of what is called Partial Products (uses positive and negative numbers) and the standard algorithm. Once you start out using Partial Differences, there is no need to switch methods in the end. The third method is something I found out about a while back. I know it to be called the "Borrow and Payback" method. It's basically the standard algorithm but notated differently. I guess I would describe it as compensation. I actually think it's clearer than the standard. I've seen the Complementary Subtraction method before, but I didn't know it had a name. It was the most confusing to me. The Austrian method is basically the same thing as the "Borrow and Payback" (compensation) method. It's just written down a bit differently. It's basically a shortcut, so there is less writing. I like it. With all of this being said, the easiest way for me to solve a subtraction problem is to "Count Up" -- a strategy used a lot of mental subtraction. Many times, I'm able to visualize a number line (and sometimes a chalkboard) in my head.
19:05 That's half-right. The complement you've done there is called "1s complement". It's used for representing negative numbers in binary. There are a few problems with it though:
1. With addition you need to do the "end-around carry" thing where you bring the 1st digit over to the end
2. There are two zeros! 000...00 and 111...11.
So people have come up with a better way to do it, "2s complement", which is almost the same as 1s complement, except the values of all negative numbers are decremented. This gets rid of the second zero, and it also has more mathematical meaning: it's almost the same as normal binary, except the first digit has a negated place value.
Also, computers don't believe in subtraction either! They just add the 2s complement instead.
Amazing Thank you
The first method is really a combination of what is called Partial Products (uses positive and negative numbers) and the standard algorithm. Once you start out using Partial Differences, there is no need to switch methods in the end. The third method is something I found out about a while back. I know it to be called the "Borrow and Payback" method. It's basically the standard algorithm but notated differently. I guess I would describe it as compensation. I actually think it's clearer than the standard.
I've seen the Complementary Subtraction method before, but I didn't know it had a name. It was the most confusing to me. The Austrian method is basically the same thing as the "Borrow and Payback" (compensation) method. It's just written down a bit differently. It's basically a shortcut, so there is less writing. I like it. With all of this being said, the easiest way for me to solve a subtraction problem is to "Count Up" -- a strategy used a lot of mental subtraction. Many times, I'm able to visualize a number line (and sometimes a chalkboard) in my head.
Hey everyone watching at school