Need Help with Uni Maths - Binary

blathnaid21

Hello,

I need to know how to count in Binary and theres loads of websites telling me how but it don't make sence to me and the leature in Uni explained it to me and i just can't get it so heres one of the websites i looked it up on so what i'm asking is, is there anyone that knows a far easier way on how to count in Binary coz i'm clueless when it comes to maths like this. All i know is that Binary is made up of 1's and 0's and 1 is on and 0 is off but to start with its 10, 100, 101 and so on and i only know that much because i saw it written but don't have a clue how. i'm told its like decimal counting which i don't know how that relates to binary so i just want to know an easy way of how do you count in Binary. Anyone?
http://www.networkclue.com/hardware/computer/binary.aspx

pwd

decimal is what we use. It is base 10. So you count up to ten before gong to the next digit.
binary is base two, so you count up to two.
0 = 0
1 = 1
10 = 2
11 = 3

Ok, well as far as I know it works like this:

It's a system to the base 2, that means that every 1 represents 2 to some power. The 1 at the rightmost represents 2^0, the next one left represents 2^1, then the next represents 2^2 etc. And 0 represents just that, 0.

So, with binary on the left, and decimal on the right, it goes like this:

0 = 0
1 (2^0) = 1
10 (2^1 + 0) = 2
11 (2^1 + 2^0) = 3
100 (2^2 + 0 + 0) = 4
101 (2^2 + 0 + 2^0) = 5
...
1010 (2^3 + 0 + 2^1 + 0) = 10
etc.

If that isn't clear enough post back and I'll try to explain it more.

LeixlipRed

Binary is a base 2 number system. i.e. it work with powers of 2. So for example 1011 in binary is (1x2^3) + (0x2^2) + (1x2^1) + (1x2^0) = 11 in decimal. So the first few binary numbers would be 0, 1, 10, 11, 100, 101, etc.

Or in more detail:

0 = 0x2^0 = 0
1 = 1x2^0 = 1
10 = (1x2^1) + (0x2^0) = 2 + 0 = 2
11 = (1x2^1) + (1x2^0) = 2 + 1 = 3
100 = (1x2^2) + (0x2^1) + (0x2^0) = 4 + 0 + 0 = 4
101 = (1x2^2) + (0x2^1) + (1x2^0) = 4 + 0 + 1 = 5

That go some way to explaining it?

Also you could be asked to turn a decimal number into binary. For example:

27 = 16 + 8 + 2 + 1 =(1x2^4) + (1x2^3) + (0x2^2) + (1x2^1) + (1x2^0) = 11011

keane2097

blathnaid21 wrote: »

Hello,

I need to know how to count in Binary and theres loads of websites telling me how but it don't make sence to me and the leature in Uni explained it to me and i just can't get it so heres one of the websites i looked it up on so what i'm asking is, is there anyone that knows a far easier way on how to count in Binary coz i'm clueless when it comes to maths like this. All i know is that Binary is made up of 1's and 0's and 1 is on and 0 is off but to start with its 10, 100, 101 and so on and i only know that much because i saw it written but don't have a clue how. i'm told its like decimal counting which i don't know how that relates to binary so i just want to know an easy way of how do you count in Binary. Anyone?
http://www.networkclue.com/hardware/computer/binary.aspx

You probably dont need to be able to count up in binary, just to be able to figure out what a binary number is in decimal and vice versa right?

Start with binary to decimal - take for example:-

1011

To convert this to binary you start with the bit farthest to the right (the least signifigant bit). You multiply this number by 2^0.

Now move left one bit. Multiply this number by 2^1.

Move left again. Multiply this bit by 2^2.

And so on moving to the left bit by bit, increasing the power of 2 you're multiplying by each time.

i.e.

(1 x 2^3) (0 x 2^2) (1 x 2^1) (1 x 2^0)

which when you multiply out gives

(8) (0) (2) (1)

Add up all these and that's your decimal value, ie

8+0+2+1 = 11


To go the other way from decimal to binary:

start off with your decimal number, let's take 11 again.

You divide the number by two, keeping track of the remainder:

11/2 = 5 - remainder 1
5/2 = 2 - remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1

now just read back up the list of remainders and that's you decimal converted to binary, ie 1011...

Does this help?

Pherekydes

Denary has ten digits, 0-9. When we count up the last digit changes until it reaches 9 and then you add an extra digit and start back at zero:

9 ---> 10

99 ----> 100

Etc.

In binary you only have two digits, 1 and 0. When the last digit changes to 1 (the highest, like 9) then add one digit and restart at zero:

11 ----> 100

111

---

> 1000

In denary, each digit stands for a power of ten: units, tens, hundreds, thousands, and so on. 111 is equal to 10^2 + 10^1 + 10^0

In binary, each digit stands for a power of two, so 111 is equal to 2^2 + 2^1 + 2^0

I hope that makes things a little clearer for you.

blathnaid21

pwd wrote: »

decimal is what we use. It is base 10. So you count up to ten before gong to the next digit.
binary is base two, so you count up to two.
0 = 0
1 = 1
10 = 2
11 = 3

So is it like this
12 = 4
13 = 5
14= 6
15 = 7
16 = 8
17 = 9
18 = 10
and so on is it?:rolleyes:

LeixlipRed

blathnaid21 wrote: »

So is it like this
12 = 4
13 = 5
14= 6
15 = 7
16 = 8
17 = 9
18 = 10
and so on is it?:rolleyes:

Please refrain from taking an attitude with a poster who was clearly trying to help. And told you the correct thing.

blathnaid21

-JammyDodger- wrote: »

Ok, well as far as I know it works like this:

It's a system to the base 2, that means that every 1 represents 2 to some power. The 1 at the rightmost represents 2^0, the next one left represents 2^1, then the next represents 2^2 etc. And 0 represents just that, 0.

So, with binary on the left, and decimal on the right, it goes like this:

0 = 0
1 (2^0) = 1
10 (2^1 + 0) = 2
11 (2^1 + 2^0) = 3
100 (2^2 + 0 + 0) = 4
101 (2^2 + 0 + 2^0) = 5
...
1010 (2^3 + 0 + 2^1 + 0) = 10
etc.

If that isn't clear enough post back and I'll try to explain it more.

I'm still Lost. I'm sorry but i'm really really bad at maths. I'm better with computers and maths is not my strongest point.sorry. If you have time could u explain it more?If u have time, if not don't worry.

LeixlipRed

There's numerous posts here explaining how it works. Have you also tried examining the wikipedia page for binary numbers? It's very clear and concise.

blathnaid21

LeixlipRed wrote: »

Binary is a base 2 number system. i.e. it work with powers of 2. So for example 1011 in binary is (1x2^3) + (0x2^2) + (1x2^1) + (1x2^0) = 11 in decimal. So the first few binary numbers would be 0, 1, 10, 11, 100, 101, etc.

Or in more detail:

0 = 0x2^0 = 0
1 = 1x2^0 = 1
10 = (1x2^1) + (0x2^0) = 2 + 0 = 2
11 = (1x2^1) + (1x2^0) = 2 + 1 = 3
100 = (1x2^2) + (0x2^1) + (0x2^0) = 4 + 0 + 0 = 4
101 = (1x2^2) + (0x2^1) + (1x2^0) = 4 + 0 + 1 = 5

That go some way to explaining it?

Also you could be asked to turn a decimal number into binary. For example:

27 = 16 + 8 + 2 + 1 =(1x2^4) + (1x2^3) + (0x2^2) + (1x2^1) + (1x2^0) = 11011

Thanks so does it go like this after 101

110
111
1000
1001
1010
1111
10000

Something like that? I'm sorry maths is not my strongest subject:cool:

blathnaid21

keane2097 wrote: »

You probably dont need to be able to count up in binary, just to be able to figure out what a binary number is in decimal and vice versa right?

Start with binary to decimal - take for example:-

1011

To convert this to binary you start with the bit farthest to the right (the least signifigant bit). You multiply this number by 2^0.

Now move left one bit. Multiply this number by 2^1.

Move left again. Multiply this bit by 2^2.

And so on moving to the left bit by bit, increasing the power of 2 you're multiplying by each time.

i.e.

(1 x 2^3) (0 x 2^2) (1 x 2^1) (1 x 2^0)

which when you multiply out gives

(8) (0) (2) (1)

Add up all these and that's your decimal value, ie

8+0+2+1 = 11


To go the other way from decimal to binary:

start off with your decimal number, let's take 11 again.

You divide the number by two, keeping track of the remainder:

11/2 = 5 - remainder 1
5/2 = 2 - remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1

now just read back up the list of remainders and that's you decimal converted to binary, ie 1011...

Does this help?

I do i need to know how to count in binary because we have to do reports so its important that i need to know how to count in binary is y i need to know.I'll get back to you again.

blathnaid21

blathnaid21 wrote: »

I'm still Lost. I'm sorry but i'm really really bad at maths. I'm better with computers and maths is not my strongest point.sorry. If you have time could u explain it more?If u have time, if not don't worry.

Yah, no problem!

Ok, every 1 that you see in binary represents a 2 to some power. Understand that? Now, in order to know what power it is, we have to assign a place value to each one. The way this is done is this:

0 in binary is just 0, zero. In binary it's used as a place marker in the same way as with normal numbers. For example, in normal numbers, we know 305 is three hundred and five because the zero is there to tell us there is nothing in the 10's space. Now, it's the same in binary: a zero is just used to tell us there is nothing in some space.

Binary works from right to left. A 1 (in binary) on its own, just means 2^0 (and we know 2^0 equals 1, by definition). 10, in binary, means 2^1 (because its one space further over from the furthest right digit). 100, in binary, means 2^2 (again, because it's one space further over than 10). And, it just continues like this. So, 10000 is 2^4 (because the 1 is 4 spaces left from the furthest right digit). It continues like this. So, just say... 10000000000, that's 2^10 (because the 1 is 10 spaces over from the furthest right digit). Now, see the way the zeros are just used as place markers, to let you know there's nothing there? So now, do you understand this much?

Next we can use a few ones in conjunction. Just say... 1010: this is 2^3 (because the furthest 1 over is 3 spaces from the furthest right digit) + 2^1 (because the next 1 is 1 space over from the furthest right digit). So, that's 2^3 + 2^1, and that equals 10. It just continues like this, for example... 101110: now, this is 2^5 + 0 + 2^3 + 2^2 + 2^1 = 32 + 0 + 8 + 4 + 2 = 46. And that's just the way it continues to work. Understand that?

Now, a few examples:

1001 = 2^3 + 0 + 0 + 2^0 = 9
1011 = 2^3 + 0 + 2^2 + 2^0 = 13
etc.

Understand? If you don't just say where you're having the problem and I'll try clarify.

994

blathnaid21 wrote: »

Thanks so does it go like this after 101

110
111
1000
1001
1010
1111
10000

Something like that? I'm sorry maths is not my strongest subject:cool:

No, remember in decimal it goes thousands-hundreds-tens-units.
So in binary it's eights-fours-twos-units.
1000 = 8
1001 = 9
1010 = 10
but 1111 = 8+4+2+1 = 15.
So from 1010 (10) there is 1011, 1100, 1101, 1110, and then 1111, 10000.

keane2097

blathnaid21 wrote: »

I do i need to know how to count in binary because we have to do reports so its important that i need to know how to count in binary is y i need to know.I'll get back to you again.

You can just use the techniques I've outlined here to calculate each number so one by one...

I still can't "count" in binary per se like I can in decimal - I'd get stuck after 11... :pac: But if I need to figure out the next number those steps I've outlined will tell me as quick as anything.

blathnaid21

LeixlipRed wrote: »

Please refrain from taking an attitude with a poster who was clearly trying to help. And told you the correct thing.

I know u were trying to help. I don't have an attitude. I just don't get it is all and i'm not great with maths but i'll get it after awhile. Sorry 4 being so slow and stupid.Thanks for ur help and i'm greatful u helped.

blathnaid21

LeixlipRed wrote: »

There's numerous posts here explaining how it works. Have you also tried examining the wikipedia page for binary numbers? It's very clear and concise.

Hi there,
y do i get the feeling that ur picking on me and sounds like u have a probelm with ppl explaining things to me?maybe i'm wrong but it just looks like that.Thanks for your help and no i didn't check them but i will okay.

LeixlipRed

I'm not picking on you. You replied to a helpful post with a "rolleyes" smiley which normally indicates contempt at what a poster has said. Then you replied to the first post in reply to yours saying you could still not understand the topic even though 8 or 9 other posts had been made prior to that. Next time you ask a question, allow people time to reply, read all those replies and then, if you still cannot understand post again. And I wasn't implying that you were "slow and stupid" as you put it.

PaulieBoy

Binary maths is simple, it's been explained to the n'th degree by the above helpful posters, you seem hell bent on ignoring their help, mocking their answers, and fixated on not learning anything at all.

You strike me as someone who has decided not to learn, which is fine, just don't waste the time of others in the process.

blathnaid21

I just want to say thanks to every1 for helping me.i get it now and it all makes sence now.thanks all.

blathnaid21

-JammyDodger- wrote: »

Ok, well as far as I know it works like this:

It's a system to the base 2, that means that every 1 represents 2 to some power. The 1 at the rightmost represents 2^0, the next one left represents 2^1, then the next represents 2^2 etc. And 0 represents just that, 0.

So, with binary on the left, and decimal on the right, it goes like this:

0 = 0
1 (2^0) = 1
10 (2^1 + 0) = 2
11 (2^1 + 2^0) = 3
100 (2^2 + 0 + 0) = 4
101 (2^2 + 0 + 2^0) = 5
...
1010 (2^3 + 0 + 2^1 + 0) = 10
etc.

If that isn't clear enough post back and I'll try to explain it more.

Thanks alot for your help.I get it now.it took me ages to work it out but i get it now so thanks for all your help.:)

blathnaid21

PaulieBoy wrote: »

Binary maths is simple, it's been explained to the n'th degree by the above helpful posters, you seem hell bent on ignoring their help, mocking their answers, and fixated on not learning anything at all.

You strike me as someone who has decided not to learn, which is fine, just don't waste the time of others in the process.

i do want to learn.i just didn't get it is all but i do now and i'm greatful for everyones help.:)

blathnaid21

LeixlipRed wrote: »

I'm not picking on you. You replied to a helpful post with a "rolleyes" smiley which normally indicates contempt at what a poster has said. Then you replied to the first post in reply to yours saying you could still not understand the topic even though 8 or 9 other posts had been made prior to that. Next time you ask a question, allow people time to reply, read all those replies and then, if you still cannot understand post again. And I wasn't implying that you were "slow and stupid" as you put it.

Thanks for your help.very helpful and thanks.i get it now.:)

.50 (MOA)

working from the right of any binary string of numbers the value of each of the 1's or 0's doubles, starting with the furthest right number having a value of 1, they are then added together. if in the binary string there is a 1 then that value for its position is included in the addition, if its value is 0 then it is not included in the addition

for instance

111111111

has a value of
256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 511

1101100

has a value of
64 + 32 + 8 + 4 + 0 + 0 = 108

1000000000000000001

has a value of
262144 + 1 = 262145


remember to start with a one at the far right and if the position has a 0 then do not include the value for that number

0's have zero value but tells you to double the value without adding it so that the next 1 has a greater value.


to add binary numbers just add the string of 1's and 0's as if it were a regular sum. then with any 2's that apper in the sum reduce it to a 0 and add 1 to the next number on the left, continuing until you only have 1's and 0's again.

for instance

101001100 + 111111010 = 212112110

(256+64+8+4) + (256+128+64+32+16+8+2)

(332) + (506) = (838)

to remove the 2's the workinng out will look like this

212112110 -> 1020121001 -> 1100200110 -> 1101000110

1101000110 = (512+256+64+4+2) =838


this might be long winded but maybe easier than struggling with 2^n

Queen-Mise

thanks .50 for that explanation. i studied this in college but have it forgotten now, i understood exactly what you said there.
and the principle is the exact same for base 4 & 8.

for some reason i wanted to know again how binary worked

MathsManiac

I know the OP has said she's sorted, and lots of the above posts have given clear information, but here's another slant on it: the original question was: how do you count in binary? Taking this completely at face value, (and not reading it as "Please explain binary" or "How do you convert between binary and decimal?") I suggest the following:

Think about it this way: how do you count in decimal? You start at 0 (or 1 if you like) and keep adding 1 to the last digit. Whenever you have to go beyond 9 (the biggest digit you're allowed) you go back to 0 and carry 1. It's the exact same in binary, except the biggest digit you're allowed is 1 instead of 9.

Start: 0
Add 1: 1
Add 1: (can't get bigger than 1, so back to 0 and carry 1): 10
Add 1: 11
Add 1: (carry again, and this time you have to carry out of the next column too, just like with 99 in decimal): 100.
...etc. for ever.

This, presumably, is how two-fingered aliens would count.

Yakuza

There are 10 kinds of people in the world, those who understand binary and whose who don't...:D

pisslips

I prefer my version:

There are 11 kinds of people in the world, those who understand binary. those who understand binary. those who understand binary

Yep a fine wife someday.......

blathnaid21

Thanks for everyone's help.

Now does anyone know how to convert decimal to hexadecimal and how to convert hexadecimal to decimal again?

Also does anyone know how to convert hexadecimal to binary also?

This is abit confusing. i got sorted in the end converting binary to decimal and vice versa so thanks everyone.

gondorff

Eat more oily fish.