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Binary!


Ste

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The best way for me to learn was just to look at it. :)

 

00000000 = 0

00000001 = 1

00000010 = 2

00000011 = 3

00000100 = 4

00000101 = 5

00000110 = 6

00000111 = 7

00001000 = 8

00001001 = 9

00001010 = 10

00001011 = 11

00001100 = 12

00001101 = 13

00001110 = 14

00001111 = 15

00010000 = 16

00100000 = 32

01000000 = 64

10000000 = 128

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Hmm this reminds me, does anyone know any other number systems? i do.. same concept, heres the 3rd number system:

1 = 1

2 = 2

10 = 3

11 = 4

12 = 5

20 = 6

21 = 7

22 = 8

100 = 9

101 = 10

 

 

And a weird one, the 11th number system:

1 =1

2=2

3=3

4=4

5=5

6=6

7=7

8=8

9=9

A=10

 

get it?

10 = 11

11 = 12

 

etc.

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Yes I completly with you On that part but which way does it go

low to high or high to low

1,2,4 Etc?

4,2,1 Etc?

449874[/snapback]

 

left to right, high to low, exactly the same as decimal...

 

but instead of hundreds, tens, units you have 4s, 2s, units

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Ok I am good On this subject now so,

 

101010010

 

512 256 128 64 32 16 8 4 2 1

 

512+0+128+0+32+0+0+2+0

 

674 decimal form.

Just so we all on right track?

 

Now HexaDecimal Im confused.

How does the place value work Similar for Hexa and Binary?

Im reading in my book that A012F

A represents 16 to the 4th Power.

 

They don't show a chart.

Edited by Ste

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hexa is easy too

 

0-0

1-1

2-2

etc

10-A

11-B

12-C

13-D

14-E

15-F

16-10

17-11

18-12

etc

31 1F

32 20

 

 

(you know i never knew it before i just learned it right now in 2 minutes :D)

 

and like... hmm... 153 = 99

255 = FF, not 15F

 

here are steps to figure it out:

1) divide whole thing by 16 and write that down

2) if what u wrote down is bigger then 16, divide it by 16 and write that down

3) repeat 2) as needed

4) write down the number u got as a hexadecimal (look at chart)

5) write down remainder as a hexadecimal

6) repeat 5) for each time u did 3)

7) done (i think)

 

:D

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hexa is easy too

 

0-0

1-1

2-2

etc

10-A

11-B

12-C

13-D

14-E

15-F

16-10

17-11

18-12

etc

31 1F

32 20

(you know i never knew it before i just learned it right now in 2 minutes :D)

 

and like... hmm... 153 = 99

255 = FF, not 15F

 

here are steps to figure it out:

1) divide whole thing by 16 and write that down

2) if what u wrote down is bigger then 16, divide it by 16 and write that down

3) repeat 2) as needed

4) write down the number u got as a hexadecimal (look at chart)

5) write down remainder as a hexadecimal

6) repeat 5) for each time u did 3)

7) done (i think)

 

:D

450116[/snapback]

 

 

So for hexiadecimal, theres only 4 characters in a set. k. and they range from 1-9, and a-f and then 10- what? But about the power of 16 thingy.

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Binary: base 2. Octal: base 8. Decimal: base 10. Hexadecimal: base 16

 

bin: 0-1, oct: 0-7, dec: 0-9, hex: 0-F (hex values=0123456789ABCDEF [F=15])

 

all above number systems read left to right, so as in 128, the largest power is to the left= 100+20+8=128dec.

 

Don't forget BCD, BCO, and BCH: binary-coded dec, oct, and hex. When you talk about binary numbers in sets (except in strait binary in bits, bytes), generally it is BCD or equivalent. BCD (and the other two) are different in the fact that instead of converting the entire number to another system by powers, the number is encoded directly to the corresponding binary number by character and put together in sets.

 

Example: 128dec to bin is=10000000; while 128dec to BCD is=000100101000. The number sets are: 1=0001, 2=0010, 8=1000; then the numbers are grouped together. BCO, binary-coded octal only uses three Binary places to represent an Oct number: 0=000, 7=111.

BCD and BCH use four: BCD: 0=0000, 9=1001; BCH: 0=0000, F=1111.

 

This number system is commonly used in computing applications where you see 4-character sets of binary numbers that represent hexadecimal numbers. Each group of four binary numbers represents a single hex number.

 

Back to normal binary, the powers are represented as: 256, 128, 64, 32, 16, 8, 4, 2, 1 in descending order as values are read highest to lowest from left to right. Do the number values for binary powers look familiar yet? Funny how it ends up working like that, huh? So not only do those numbers (converted to dec) look so familiar in computing; and in fact makes BCD and the others possible, especially hex, workable.

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yes binary is a 2 digit number system. unlike the decimal number system which uses 0-9, in binary there is only 1 and 0. (On and Off).

 

for any 8 bit (or less than 8 bit) binary number (like 10101010 or 1010) you can use this chart :

128_64_32_16_8_4_2_1

 

see the chart has 8 parts, they are: 128, 64, 32, 16, 8, 4, 2, 1

 

lets try using the chart with this 8 bit binary number, 11111111. We will plug it in below:

128_64_32_16_8_4_2_1

__1__1__1__1_1_1_1_1 =255

so 11111111 = 255

because for every 1 you add the number above it. so:

adding 128+64+32+16+8+4+2+1 = 255

 

heres another example:

lets use 00001001 ( which is the same as 1001)

plug it into the chart below:

 

128_64_32_16_8_4_2_1

__0__0__0__0_1_0_0_1 =9 (8 + 1)

so 1001 = 9 (8+1)

 

here is another small chart:

binary_____decimal

00000001 = 1

00000010 = 2

00000100 = 4

00001000 = 8

00010000 = 16

00100000 = 32

01000000 = 64

10000000 = 128

 

here is a short chart :

see a pattern?

________________________

binary_____decimal

00000001 = 1

00000010 = 2

00000011 = 3 (2+1)

00000100 = 4

00000101 = 5 (4+1)

00000110 = 6 (4+2)

00000111 = 7 (4+2+1)

00001000 = 8

00001001 = 9 (8+1)

00001010 = 10 (8+2)

00001011 = 11 (8+2+1)

00001100 = 12 (8+4)

00001101 = 13 (8+4+1)

00001110 = 14 (8+4+2)

00001111 = 15 (8+4+2+1)

00010000 = 16

00010001 = 17 (16 +1)

ect.

 

If you get into subnetting, its important to know your powers of 2. (2^x)(2 to the x)

 

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

2^8 = 256

2^9 = 512

2^10 = 1024

2^11 = 2048

2^12 = 4096

ect.

 

hope this helps someone. or not. :ph34r:

 

there are only 10 types of people in the world, those who dont understand binary and those who do.

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Ya i Understand that, I just don't understand Hexdecimals now.

 

what if its more then 9 chracters though, for binary do the powers contine

 

like

 

1024,512,128,64,32,16,8,4,2,1

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Oct: 0-7 hex: 0-F (0-15 decimal) BCD: binary coded decimal. BCH and BCO (terms only used for illustration): binary coded hexadecimal and octal.

 

You can convert hexadecimal strait to binary, but using hex powers do to so is a bit tricky. I find it easier to use BCH, but the process from hex-bin from powers is: 400, 200, 80, 40, 20, 10, 8, 4, 2, 1 hex (see the pattern?). Adding them up can be a little tricky, which is why I use BCH. hex-bin example: FF hex (255 dec) comes out to 11111111. The fast way to find that is to use BCH: F=1111, as unlike dec, every hex character corresponds directly to a bin number up to 1111. Octal also corresponds directly with BCO with 3 character bin: 7=111, so 777=111111111. Decimal cannot be done that way, as the highest dec number 9=1001, except to find BCD. But, decimal is far easier to convert using powers: ex. 64, 32, 16, 8, 4, 2, 1.

 

So, dec-bin should be found using powers, unless trying to convert to BCD (if trying to subtract BCD, the number has to be shifted by bin 3.... but that's another story altogether). Hex and Oct should be found using BCH and BCO, BCH: F (15 dec)=1111, all numbers keeping all four corresponding bin numbers except any leading 0's. The same for Oct, except that only three bin numbers are used per octal character, as the highest oct number 7=111.

 

I hope that helps.

 

Edit: I forgot to add this example: unless you are trying to find BCD, any leading zeros should be dropped. Example: CDC hex is 110011011100 bin while 2DC is 1011011100; the number works out to 001011011100, but the first two zeros are dropped.

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Ok I got it now, I was just number crunching numbers for like an hour between Binary and HEadecimals for fun.

 

My only question would be, is the length of a binary and hexadecimal limited like

binary is limmited to 9, 0's and 1's and Hexa is limited to 5 charcaters, becaise if its true then Im lost again,

 

 

Can't they go on and on forever

like

0010101010101010101010101010101010101010101010101010101010111111111111111000100101010101

 

Cause it makes more since when I do the columns.

 

Btw the largest number i got for hexadecimal was

F92D39

 

and that was

16,330,041

 

Am I right?

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Yes, the numbers can go on forever, it's just that your calculator only has so many registers and character display spaces. When a number becomes to big to be done on a calculator, you have to turn to paper.

 

Edit: you are correct. One easy way to convert hex to dec is to go though binary.

 

F92D39 hex=1111,1001,0010,1101,0011,1001 bin=16330041 dec (commas inserted to better show BCH)

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