Question

Hey I was just wondering...

Answer 1

I was trying to count in base 2 like 1, 2, 10, 11.....and so on.
Can u all help if u know it

Answer 2

it goes: 0, 1, 10, 11, 100, 101, 111, etc

the digit "2" does not exist in base 2

Answer 3

this is analogous to saying that the digit "10" doesn't exist in base 10

the digits "1" and "0" do, but not "10"

Answer 4

base 2 is also known as the binary counting system which is used extensively in computing (since 0 represents "off" and 1 represents "on" in a circuit)

Answer 5

oh okay, so then it is
111, 1001, 10000, 10001 etc
correct?

Answer 6

oh okay
that's interesting too

Answer 7

111, 1000, 1001, 1010, 1011, 1100, 1101, 1111, and so on

here's a much longer list

http://www.minus40.info/sky/binary.html

Answer 8

the basic idea is that 1+1 = 10 in base 2

Answer 9

and you use this idea to generate the next number (just add 1 to the previous number to get the next). Don't forget to carry

Answer 10

hmm..yeah
that makes sense
and how would u count in base 7?
does 6 not exist like...
0,1,2,3,4,5,6,10,11,12,13,14,15,16,100

Answer 11

6 is the largest digit in base 7

7 is the largest digit in base 8

and so on (you go as high as the base, exclude the base itself)

Answer 12

you have the right count though for base 7

0,1,2,3,4,5,6,10,11,12,13,14,15,16,100, ...

Answer 13

okay
and one more thing, if u want to explain.....
how do we take 15 (in base 10) and turn it in base 7 number

Answer 14

I have some clue but not a whole lot

Answer 15

First divide 15 by 7

15/7 = 2 remainder 1

then you take that quotient (2) and divide it by 7

2/7 = 0 remainder 2

notice how the denominator is always the base (7)

Answer 16

so in summary, we have


15/7 = 2 remainder 1
2/7 = 0 remainder 2

read the remainders in reverse. So read starting at the bottom and read up: 21


Therefore, 15 in base 10 = 21 in base 7

You'll often see it in this notation

\[\Large 15_{10} = 21_{7}\]

Answer 17

oh and you stop when you get a quotient of 0

Answer 18

something to check your work with

http://korn19.ch/coding/base_converter.php

just don't rely on it completely (use it as a check, not something to do all your hw)

Answer 19

so then 30 in base 7 would be... 42 ?

Answer 20

going from base 7 to base 10 uses a different method

Answer 21

this is not my homework :)
jst curious
thanks for the links tho

Answer 22

oh you want to go from 30 base 10 to a number in base 7?

Answer 23

no no 30 is in base 10

Answer 24

yeah

Answer 25

ok, then yes

\[\Large 30_{10} = 42_{7}\]

Answer 26

and 28 (in base 10) would be 4 in base 7 ?

Answer 27

no

Answer 28

28/7 = 4 remainder 0
4/7 = 0 remainder 4

read remainders in reverse to get 40

\[\Large 28_{10} = 40_{7}\]

Answer 29

4 in base 7 = 4 in base 10 since 4 is less than 7

Answer 30

again that calculator will confirm

Answer 31

okay
so how do u do the opposite? convert base 7 numbers to base 1o nos. ?

Answer 32

give me an example to work with, which number do you want to use?

Answer 33

34

Answer 34

Let's focus on the base 10 number system

Answer 35

34 in base 10 means 30 + 4

or

3*10 + 4*1

Answer 36

notice how the 10 pops up

Answer 37

and how 1 = 10^0

Answer 38

so 34 = 3*10^1 + 4*10^0

Answer 39

this breakdown is handy to convert from base 7 to base 10

Answer 40

so now let's say we have 34 in base 7

34 base 7 = 3*7^1 + 4*7^0

34 base 7 = 3*7 + 4*1

34 base 7 = 21 + 4

34 base 7 = 25 base 10

Answer 41

another example

convert 345 in base 7 to base 10


345 base 7 = 3*7^2 + 4*7^1 + 5*7^0

345 base 7 = 3*49 + 4*7 + 5*1

345 base 7 = 147 + 28 + 5

345 base 7 = 180 base 10

Answer 42

this part is a little confusing

Answer 43

look at my second example

Answer 44

hmm...okay maybe i get it now

Answer 45

it's strange at first, I agree

Answer 46

but with enough practice, it's not too bad

Answer 47

i bet i will practice n get it

Answer 48

ok great

Answer 49

thanks :)
u must be in like comp major or something...u r smart

Answer 50

I took a bunch of computer science courses, but I'm actually a math education major

Answer 51

That's great.