Converting decimal to binary?

py2006 · 12-12-2006 04:14PM #1

Hi folks,

I am working away on some questions that will no doubt come up in an exam next year.

The first is converting a decimal number to a binary number.

Lets say 221:

221/2 = 110 remainder = 1
110/2 = 55 remainder = 0
55/2 = 27 remainder = 1
27/2 = 13 remainder = 1
13/2 = 6 remainder = 1
6/2 = 3 remainder = 0
3/2 = 1 remainder = 1
1/2 = 1 remainder = ???

Now I know you reverse the numbers to get the binary but I am not sure what the first number is

?1011101

Help meeeeeeeeeeeeeeeeeeee!

stipey · 12-12-2006 04:25PM

I didn't read this fully but this might help...

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

Noelie · 12-12-2006 04:30PM

if it's a odd decimal number the last digit must always be a '1'

py2006 · 12-12-2006 04:36PM

Noelie wrote:

if it's a odd decimal number the last digit must always be a '1'

Ah I see! I went to a site that automatically converts them and it had a 1 there. I couldn't figure out why!

Thanks

py2006 · 12-12-2006 04:40PM

What about the reverse? Binary to decimal?

1010100

Noelie · 12-12-2006 04:45PM

is that read left to right or right to left? i could never remember
but i make that out to be 21

py2006 · 12-12-2006 04:48PM

Noelie wrote:

is that read left to right or right to left? i could never remember
but i make that out to be 21

I don't know! I was hoping you could tell me!

py2006 · 12-12-2006 04:54PM

py2006 wrote:

I don't know! I was hoping you could tell me!

I think there answer is actually 84! not sure!

Noelie · 12-12-2006 04:54PM

well i'm reading it from the left as the lsb, but i could be wrong it's been years since i done any of this stuff.
the lsb is 1, then 2 then 4, every next bit represents twice the previous so you'd have
1 2 4 8 16 32 64 128 256 512
1 0 1 0 1 0 0
so you add 1 + 4 + 16 and get 21.

but if the 0 on the rigth is the lsb you get
1 2 4 8 16 32 64 128 256 512
0 0 1 0 1 0 1
which would be 4 + 16 + 64 = 84

py2006 · 12-12-2006 04:56PM

py2006 wrote:

I don't know! I was hoping you could tell me!

I think there answer is actually 84! not sure!

Noelie · 12-12-2006 05:00PM

just looked about a little and it's read from right to left, so the lsb is 0, making 84 the correct answer

Smellyirishman · 12-12-2006 05:03PM

To go from binary to decimal

The far right digit it 2^0 or 1,
the one left to that is 2^1 or 2,
left of that is 2^2 or 4.
left of that is 2^3 or 8.
etc...

So, if you have 101 as your binary number then 2^0 is "on" and 2^2 is "on" so 1+4 = 5.

In your example, it's.... nm, check out Noelie's explaination. (I am pretty sure 2^0 is the rightmost bit)

vallo · 12-12-2006 10:00PM

A minor point but can't you check it on your calculator?
You can do binary, octal, dec, hex conversions on any decent calculator - even the Microsoft(R) calculator can do it.

py2006 · 13-12-2006 12:07AM

vallo wrote:

A minor point but can't you check it on your calculator?
You can do binary, octal, dec, hex conversions on any decent calculator - even the Microsoft(R) calculator can do it.

Yes, but they can't be brought into the exam!

dingding · 13-12-2006 12:14AM

Try this game for practice.

http://forums.cisco.com/CertCom/game/binary_game_page.htm?site=celc

Cheers

Pherekydes · 13-12-2006 10:25AM

py2006 wrote:

Hi folks,

1/2 = 1 remainder = ???

(

1/2 = 0 remainder 1.

This is your one mistake. Bí cúramach!

Pherekydes · 13-12-2006 10:31AM

For binary to decimal conversion:

1011:

= 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0)

= 8 + 0 + 2 + 1

= 11

Start on the right. The first bit is two to the power of zero, the next one is two to the power of one and so on.

py2006 · 13-12-2006 12:07PM

Thanks guys! does the symbol ^ mean to power of?

Pherekydes · 13-12-2006 01:47PM

py2006 wrote:

Thanks guys! does the symbol ^ mean to power of?

Yes.

Converting decimal to binary?

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