Two's Complement Part 1 - An Introduction

An introduction to two's complement representation of signed integers.

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[MrLemonyFresh]

Don't you mean when you add a bit it's double minus 1?

[protowise]

@MrLemonyFresh thanks for the question. The short answer is no. Here's the longer version: when you add a bit to the number of bits in your system, the number of values you can represent is doubled. For example, if I have a 1 bit system, the only values I can represent are 0 and 1, i.e. 2 values can be represented in a 1 bit system. If I add bit to the system and make it a 2 bit system, I can now represent 4 values 00,01,10,11. 3 bits, 8 values 000,001,010,011,100,101,110,11­1, and so on...

[MrLemonyFresh]

@protowise I thought that 111 equalled 7 (1+2+4) but wait, if i added another bit (8) wouldn't that be one more than doubled since 7 doubled is 14 and 1111 is 15?

If I'm wrong, don't worry about explaining though, I just finished my last ever software design exam and I want to stick by what i said about not ever having to think about software design again XD or at least until it by chance comes up when I'm 3d animating...

[protowise]

@MrLemonyFresh It's no problem, don't mind clarifying. You are talking about adding a bit to a specific number (111 in your example). If you add a 1 bit to a number like you did, you effectively double the number + 1 as you correctly noted. By contrast if you add a 0 bit to a number you simply double the number. In my example above, I'm talking about the "number space", not a specific number. The number space is the total number of values you can represent with a given number of bits.

[ericcaines]

Not really helpful... Wanted to learn how to subtract 8 bit binary but ... w/e ill look elsewhere

[protowise]

FYI...the concepts and methods are exactly the same for 8 bit or any other number of bits. 3 bits was used for convenience.

[dallashawks]

Wow. You explained this a thousand times better than my CS professor. Thank you!

[co3vorden]

Thanks a lot!

[SouthMoneyBoss]

Great start, now I need to watch part 2.

[marcdugy]

trololololoolol



[Dosalt]

Very helpful. Thanks lord.

[MagikGimp]

And this is why I can't be a computer engineer. I can use computers very well but sod all this maths. Actually, I could probably do it if I tried but ugh.

[LightningHexagon]

Great!

[jitendra4272]

thank u so much.......

[GM608]

Two's Complement 7:25

[lightswitchlarry]

Amazing, you need to make more videos! Not only are you very smart, but the way you talk and explain things is just amazing.

[0kazaki]

THANK YOU!