# Counting In Binary

Discussion in 'A+ Certification' started by Raymond, Mar 3, 2004.

1. ### RaymondGuest

I know that understanding how to count in binary is not going to help in
fixing computer, but I just want to know. I don't understand the concept of
counting in binary. Can anyone tell me how it work counting from 1 to 10?

Raymond, Mar 3, 2004

2. ### SlammerGuest

IT WILL HELP WHEN YOU GET INTO SUBNETTING NETWORKS

--
Slammer
MCSA, CNA, iNet+, Server+, Net+, A+
"Raymond" <> wrote in message
news:...
> I know that understanding how to count in binary is not going to help in
> fixing computer, but I just want to know. I don't understand the concept

of
> counting in binary. Can anyone tell me how it work counting from 1 to 10?
>
>

Slammer, Mar 3, 2004

3. ### GeoffGuest

Slammer wrote:
> IT WILL HELP WHEN YOU GET INTO SUBNETTING NETWORKS
>
>> I know that understanding how to count in binary is not going to
>> help in fixing computer, but I just want to know. I don't
>> understand the concept of counting in binary. Can anyone tell me
>> how it work counting from 1 to 10?

indeed yes
binary helps lots when working out subnet masks and the like
try work this one:

255.255.255.1
or
0.255.255.255
or
64.64.64.64

enjoy

Geoff, Mar 3, 2004
4. ### Tom MacIntyreGuest

On Wed, 03 Mar 2004 23:44:27 GMT, "Billy" <> wrote:

Almost...

>0 = 0

1=1
>10 = 2
>11 = 3
>100 = 4
>101
>110
>111
>1000
>1001
>1010
>1011
>1100
>1101
>1110
>1111 = 15
>Hopefully no mistakes, in a hurry, gotta run.

Just one, but then you ended up with accumulation error.

The numbers ending in 0 are even numbers, odd when they end in 1.

Tom

>
>"Raymond" <> wrote in message
>news:...
>> I know that understanding how to count in binary is not going to help

>in
>> fixing computer, but I just want to know. I don't understand the

>concept of
>> counting in binary. Can anyone tell me how it work counting from 1 to

>10?
>>
>>

>

Tom MacIntyre, Mar 4, 2004
5. ### Jonathan MilesGuest

If you have the number 603 (for example) in decimal it represents :

6 x 100 plus
0 x 10 plus
3 x 1 = 603

| 100's | 10's | 1's |
| 6 | 0 | 3 |

If you have the binary number 110101 it represents :

1 x 32 plus
1 x 16 plus
0 x 8 plus
1 x 4 plus
0 x 2 plus
1 x 1 = 53 in decimal

| 32's | 16's | 8's | 4's | 2's | 1's |
| 1 | 1 | 0 | 1 | 0 | 1 |

Hope this helps ) (and I hope it posts ok!)

JM

"Raymond" <> wrote in message
news:...
> I know that understanding how to count in binary is not going to help in
> fixing computer, but I just want to know. I don't understand the concept

of
> counting in binary. Can anyone tell me how it work counting from 1 to 10?
>
>

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Jonathan Miles, Mar 4, 2004
6. ### David BlandIIIGuest

Look at it like this Raymond:

As you know, binary uses only two digits to represent numbers whereas base
10 (what we use) uses 10 digits (0 - 9) to represent any number. In the
decimal
(base 10) number system we can use ten different digits to represent a
number
value before we have to go into the next column to the left. Ex:

We can represent any number from 0 to 9 by placing it's symbol in the 1s
column
before we have to go over one place to the left to represent units of ten:

1000s 100s 10s 1s
------ ----- ---- ---
1
2
3
4
.
.
9
1 0

As the numbers get larger we fill the columns up until we use up ten digits
(0 - 10)
and then move one place to the left again. Simple, right?

Well, in binary we only have two digits we can use (0 and 1) before we have
to
move one place over to the left in representing larger and larger numbers.
With
the decimal system having ten digits, each column represents units of ten.
With
binary, each column represents units of two. Thus instead of each column
(place
holder) having representing ten values, as in decimal, they only represent
two
values (binary). Thus instead of having 1, 10, 100, 1000 (from right to
left),
you have 0, 2, 4, 8, 16, etc. You may ask why not 2,4,6,8,10 etc. instead?
The
answer is that base 10 (decimal) means that each column of numbers
represents
powers of ten (thus 1, 10, 100, 1000). Similarly base 2 (binary) represents
powers of 2 (thus 0,2,4,8,16,32). Each column doubles the previous value.
Therefore when we write numbers in the decimal system, the columns look like

1000 100 10 1
----- ----- --- ---

But when we count in binary the columns look like

........ 32 16 8 4 2 0
--- -- -- -- -- --

If you simply remember to increase the placeholder by a factor of two as you
move to the left, you can convert any decimal number into its binary
equivalent.
In binary (as so with computers) 0 represents no and 1 represents yes.
Therefore
to write a number in binary, you simply put a 1 in the proper placeholder
column
that represents a value that is a component of the total number. To clarify,
if you're
writing the number ten in binary you would simply start at the left and
moving towards
the right (the smaller number) "does this number (represented by the column
or
placeholder value) fit into ten. Looking at our placeholder columns above 16
is
larger than ten, so that column has a value of 0 (no). Does 8 (the next
value to the
right) go into 10. The answer is yes so you would place a 1 (yes) in the
eight's
column. Since we have represented the value eight that leaves you only with
the
value two to come up with your ten. So, moving to the right, you ask
yourself "does
4 go into 2 (the value left that we have to account for)? The answer is no
so you
put a 0 (no) in the four's column. The next column to the right is the two's
column.
Does 2 go into 2? Yes, so we put a 1 (yes) in the two's column. That gives
you
your value of ten so you simply place a 0 in any remaining column to the
right to
complete your binary number. Thus the number 10 in binary would be:

................. 32 16 8 4 2 0
--- --- -- -- --- --
0 0 1 0 1 0 or just 1010 since you leave
off preceding
zeroes just like in
decimal format.

Using this method, the following decimal numbers would look like this:

64 32 16 8 4 2 0
---------------------- = decimal 72 (64 + 8)
1 0 0 1 0 0 0 1001000

64 32 16 8 4 2 0
-- -- -- -- -- -- -- = decimal 28 (16 + 8 + 4)
0 0 1 1 1 0 0 11100 (leave off preceding 0s)

16 8 4 2 0
-- -- -- -- -- = decimal 5 (4 + 1)
0 0 1 0 1 101 (in binary, the 0 place always has
a value of 1
thus any odd number will
always end with the
number 1 when written in
binary)

16 8 4 2 0
--- --- -- -- --- = decimal 17 (16 + 1)
1 0 0 0 1 10001

Get it? Though confusing as hell to explain, it's actually quite easy when
you
do it this way. Just lay out your colums of powers of two in descending
(left
to right) order and place your true (1) values under the appropriate
columns.
All the rest of the values are 0. The binary number starts with the first 1.
Voila. Hope that helps.

D. Bland

"Raymond" <> wrote in message
news:...
> I know that understanding how to count in binary is not going to help in
> fixing computer, but I just want to know. I don't understand the concept

of
> counting in binary. Can anyone tell me how it work counting from 1 to 10?
>
>

David BlandIII, Mar 4, 2004
7. ### Tom MacIntyreGuest

On Thu, 04 Mar 2004 02:50:44 GMT, "Billy" <> wrote:

>Major SNAFU, good catch.
>Skipped #1
>or deleted it when I added the decimal =,
>Thanks Tom.

Thank you.

Tom

>
>"Tom MacIntyre" <> wrote in message
>news:...
>> On Wed, 03 Mar 2004 23:44:27 GMT, "Billy" <> wrote:
>>
>> Almost...
>>
>> >0 = 0

>> 1=1
>> >10 = 2
>> >11 = 3
>> >100 = 4
>> >101
>> >110
>> >111
>> >1000
>> >1001
>> >1010
>> >1011
>> >1100
>> >1101
>> >1110
>> >1111 = 15
>> >Hopefully no mistakes, in a hurry, gotta run.

>>
>> Just one, but then you ended up with accumulation error.
>>
>> The numbers ending in 0 are even numbers, odd when they end in 1.
>>
>> Tom
>>
>> >
>> >"Raymond" <> wrote in message
>> >news:...
>> >> I know that understanding how to count in binary is not going to

>help
>> >in
>> >> fixing computer, but I just want to know. I don't understand the
>> >concept of
>> >> counting in binary. Can anyone tell me how it work counting from 1

>to
>> >10?
>> >>
>> >>
>> >

>>

>

Tom MacIntyre, Mar 6, 2004
8. ### Tom MacIntyreGuest

On Thu, 4 Mar 2004 20:57:13 -0500, "Kathy" <> wrote:

>It's only 2.... They are rather good
>
>"FredG" <> wrote in message
>news:...
>>
>> "Kathy" <> wrote in message
>> news:...
>> > These two sites are good for learning to count in binary.

>>
>> Surely that should be 10 sites
>>
>>

>

You're not thinking in binary, Kathy...

Tom

Tom MacIntyre, Mar 6, 2004
9. ### Tom MacIntyreGuest

On Thu, 4 Mar 2004 16:50:54 -0600, Heath <>
wrote:

>
>There are 10 types of people in the world. Those that know binary and
>those that don't...

Somewhat related...how can Hallowe'en be equal to Christmas? Scroll
down for the answer, or Rot 13 for those who use it.

BPGny 31 = QRPvzny 25

OCTal 31 = DECimal 25

Tom MacIntyre, Mar 6, 2004
10. ### Gordon FindlayGuest

On Thu, 04 Mar 2004 04:36:49 GMT, "David BlandIII" <>
wrote:

>Look at it like this Raymond:
>
>As

<snip>

>powers of ten (thus 1, 10, 100, 1000). Similarly base 2 (binary) represents
>powers of 2 (thus 0,2,4,8,16,32). Each column doubles the previous value.
>Therefore when we write numbers in the decimal system, the columns look like
>
>1000 100 10 1
>----- ----- --- ---
>
>But when we count in binary the columns look like
>
>....... 32 16 8 4 2 0
> --- -- -- -- -- --

Make that 32 16 8 4 2 _1_

and similarily elsewhere in your post.

Gordon

Gordon Findlay, Mar 6, 2004
11. ### Jonathan MilesGuest

> > > > >> Surely that should be 10 sites
> > >>
> > >>
> > >

> >
> > You're not thinking in binary, Kathy...
> >

Surely that should be 00001010 sites then?

)

JM

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Jonathan Miles, Mar 6, 2004
12. ### Tom MacIntyreGuest

On Sat, 6 Mar 2004 13:19:46 -0000, "Jonathan Miles"
<jonathanmilesnospam@uk2dotnet> wrote:

>
>> > > > >> Surely that should be 10 sites
>> > >>
>> > >>
>> > >
>> >
>> > You're not thinking in binary, Kathy...
>> >

>
>
>Surely that should be 00001010 sites then?
>
>)
>
>JM
>
>
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>Outgoing mail is certified Virus Free.
>Checked by AVG anti-virus system (http://www.grisoft.com).
>Version: 6.0.596 / Virus Database: 379 - Release Date: 27/02/2004
>

Darn it Jonathan...you beat me to it!

Tom

Tom MacIntyre, Mar 6, 2004
13. ### DrewGuest

Re: Counting In Binary - An old trick from a Fortran programmer

I had an old Fortran guy show me the EASIEST way to count in binary. I'll
try to explain it. It's easy and you don't need to remember the "place

Take any binary number, like 01010111;

Start on the LEFT (that's not a mistake, left not right) and find the first
"1" and count it as "1".

Move one place to the RIGHT and double your previous score if it's a "0" or
double it + 1 if it's a "1". In the example above, it's a 0, so double your
previous 1, so the answer is now 2.

Continue moving one place at a time, doubling your number if that particular
digit is a 0, or double + 1 if it's a 1.

So for the example above, working from left to right, starting at the first
"1",

Count 1 and move to the next place;
Now 2 (Double answer from above because it's a 0) and move to the next
place;
Now 5 (Double 2 and add 1 because it's a 1) and move to the next place;
Now 10 (double 5 because it's a 0) and move to the next place;
Now 21 (Double 10 and add 1 because it's a 1) and move to the next place;
Now 43 (Double 21 and add 1 because it's a 1) and move to the next place;
Now 87 (Double 43 and add 1 because it's a 1) and you're done, the number
equals 87.

It sure beats adding 64 + 16 + 4 + 2 + 1

I hope I explained that well. It's easier to do on a dry-erase board because

Doug

From
"Raymond" <> wrote in message
news:...
> I know that understanding how to count in binary is not going to help in
> fixing computer, but I just want to know. I don't understand the concept

of
> counting in binary. Can anyone tell me how it work counting from 1 to 10?
>
>

Drew, Mar 7, 2004
14. ### Jonathan MilesGuest

Re: Counting In Binary - An old trick from a Fortran programmer

Thanks for sharing that, I like it a lot!!

)

JM

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Jonathan Miles, Mar 7, 2004