Okay, shall we start and maybe we can get through the material today so that we can

start programming next week.

Who remembers this?

Who remembers this?

Yeah, how to represent numbers and how to count them with them in binary.

Yeah, so binaries should be something that you can convert more or less in your head,

at least I mean I would say three or four positions you should be able to recognize

by just seeing them because they can be quite effective in programming hardware.

Who can explain this?

Okay, so what happens here?

Anybody?

No wrong answers, okay, just try.

It has an extra integer number.

Sorry again?

It has an extra integer number on the right, like minus eight is the extra number that's

on there.

Okay, so extra number is a good point.

We need to find some.

It is actually minus seven to seven, but extra eight is included.

Okay, but what do we do with the eight?

So we have identified eight is probably the largest number we can represent with four

digits, with both binary digits.

What do we do with the eight if we use excess notation?

It's like, yeah, how do you move?

How do you move mathematically?

Yeah, what's your answer?

So you can add, subtract, yes, excess basically means shift and shift in this sense means

we subtracted, right, so that every signed notation now is shifted so that the smallest

bit pattern, yeah, so that the smallest bit pattern represents the smallest decimal number.

It just makes sorting easier.

It's not as intuitive anymore because zero doesn't mean zero anymore, but we can sort

them now quite easily because the larger the binary numbers, no matter if signed or not

unsigned, the larger the decimal representation for it.

Okay, so keep that in mind.

That's probably, it sounds awkward, but we come to this in just a moment.

Yeah.

So I just see that there is just two one positive or is that just a mistake or in the excess

state you have minus two one, so it's minus one and it's just a mistake or is the way

it's supposed to be?

Okay, very spot on.

Yes, right.

Okay.

Yes, that should be minus one.

It's just a table, right?

Okay, no, yeah, that would be my question.

Yeah, yeah, yeah.

No, no.

So, but this is also an interesting point here.

We have one additional number we can represent, minus eight, and that only goes to seven.

And the other representations, we have things like plus zero and minus zero.