How are demicals represented by the binary numbering system?

Question

I've been labouring over this for about a week, but I can't get my head around radixes. I need a clear, SIMPLE explanation.

Answer 1

try these

http://en.wikipedia.org/wiki/Binary_numeral_system#Decimal

http://www.wikihow.com/Convert-from-Decimal-to-Binary

Answer 2

Look at the decimal system : 215 means what?
it means 2 * 10 ^2 + 1 * 10 ^ 1 + 5 * 10 ^ 0
which is 2 * 100 + 1 * 10 + 5 * 1
which is 215

It's the same in binary except we're using powers of two instead of powers of ten

so 110011
is the same as
1 * 2 ^ 5 + 1 * 2 ^ 4 + 0 * 2 ^ 3 + 0 * 2 ^ 2 + 1 * 2 ^ 1 + 1 * 2 ^ 0
which is
1 * 32 + 1 * 16 + 0 * 8 + 0 * 4 + 1 * 2 + 1 * 1
or 51

Does that make sense?

Answer 3

ok, depending on what the number your trying to find, a simple explanation. Binary is made up from a series of noughts and ones, the higher the number, the longer the binary string. basing this answer on a an 8 digit string .....
00000001 = 1
00000010 = 2
00000011 = 3
00000100 = 4
00000101 = 5
00000110 = 6
00000111 = 7
00001000 = 8
and so it goes....
00010000 = 16
00010001 = 17.....
basicaly the first binary digit denote a 1, second a 2, third a 4, 4 th an eight, it doubles after every digit.
so 1000000000 would be 512, 1000000001 would be 513
so at 10 digits 1010101010 is 682.
any help.......mail me for more help, or mail me the dec and i'll send the bin..........

Answer 4

I am not a math wiz by any means, but the question peaked my interest.

I used to teach ATM and Alarm class's. Fault codes were displayed in Hex so I would spend time on showing how to do the conversions. A refresher in binary came first as most of the guy's had learned that in military or college electronics. I saw the struggle in some really smart faces.

All that said I hope this link helps.

Answer 5

I am wondering if you mean numbers < 1
The key thing to remember about bases is that they are very easy, if you are getting confused then you are trying to make it more complex than it is. Many people have routinely used bases other than 10 for years without even noticing such as pounds and ounces which is base 16 or feet and inches which is base 12.
Mentally the key step is being able to read 10 as one x base + zero times one and not as ten

In base ten five plus six = eleven or written in digits 5+6=11
In base two five plus six is still eleven, written in digits this is 101+110=1011. Mentally you should still read the digit version as five plus six because that is what it is
The two sums are identical.
When dealing with decimals use exactly the same rules as you are used to

In base ten five divided by two = two and a half = 5/2=2.5 (two times one plus five times one tenth)
In base two this is 101/10 = 10.1 (one times two plus one times one half)

Base ten moving left one digit multiplies by ten, moving right divides by ten.
Base two moving left one digit multiplies by two, moving right divides by two.

I can feel myself falling into the trap of making it sound complex. Just try and remember that the rules in base ten are identical to the rules in any other base. The simplest base to work in is base two, try some multiplications and divisions in base two just to get the feel of it.

Answer 6

In the decimal system it's tenths, hundredths, and thousandths going left to right from the decimal point. So obviously in binary it's halves, fourths, eighths, sixteenths, thirty-secondths, etc.from the binary point.

Answer 7

Sorry , I wouldn't have an idea but thank you for asking the question. I am about to learn with you.....Thank's for all the links people.

Answer 8

Base two""""""""""""Base ten
16""8""4""2""1"""""10""""1
""""""""""""""""1""""""""""""1
"""""""""""""1""0""""""""""""2
"""""""""""""1""1""""""""""""3
""""""""""1""0""0"""""""""""4
""""""""""1""0""1"""""""""""5
""""""""""1""1""0"""""""""""6
Hope you can continue.