Signed-digit representation

Have you ever played with LEGO blocks and built numbers? Signed-digit representation is like building numbers using LEGO blocks, but there are some special rules you have to follow.

First, you can only use 0, 1 and 2 LEGO blocks. No other numbers are allowed.

Second, each block must have a sign attached to it, either + or -. If the block has a + sign, it means it is a positive number. If it has a - sign, it means it is a negative number.

Now, let's say we want to build the number 7 using these special LEGO blocks. We could do it like this:

+2 +2 +2 +1

See how we used four +2 blocks and one +1 block to make the number 7? That's the basic idea behind signed-digit representation.

But what about negative numbers? Well, we just use blocks with - signs instead of + signs. Let's say we want to build the number -5. We could do it like this:

-2 -2 +1

See how we used two -2 blocks and one +1 block to make -5? That's how signed-digit representation works.

One of the cool things about signed-digit representation is that it allows us to do some math operations really quickly. For example, if we want to add 7 and -5 together, we can just line up the blocks like this:

+2 +2 +2 +1
-2 -2 +1

And then we can cancel out any pairs of blocks that have the same value but opposite signs. In this case, we can cancel out two +2 blocks and two -2 blocks, which leaves us with:

+1 +1

So 7 + (-5) = 2, just like we learned in school!

Overall, signed-digit representation is a fun way to build and manipulate numbers using special LEGO-like blocks with + and - signs. It's a bit like learning a secret code that can make math problems easier to solve!