Adding Binary Numbers....??

Question

Alright. I have to convert two decimal numbers into binary. And then add them together. Then I have to show that the sum of the binary numbers is = to the sum of the decimal numbers.

Ok the numbers are 257 & 431. Their sum is 688.

I am sooo close on this but for some reason I'm just one number off. Can you please help me???? PLEASE??

Also am I right in that 688= 1010110000?

THanks in advance.

Ya'll FREAKEN ROCK!!! THank you sooooo much. I totally get where I made my mistake now. Two does not go into 3, 2 times... I'm a dork. Thanks!!!

Answer 1

OK let's see if we can get it for you:

Base powers work like this

10 to the 0 power = 1
10 to the 1 power =10
10 to the 2 power =100
10 to the 3 power =1000.
10 to the 4 power =10000 etc., etc.

So when we say you have a number 4,256 that is like saying I have the following

4 x 10^3 = 4000
2 x 10^2 = 200
5 x 10^1 = 50
6 x 10^0 = 6

Add them up you get 4,256. Note the notation ^ means to the power of.

OK - now lets try the base power of 2.

2^0 = 1
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

OK
Picture this for your number
------------------------------...
2^6 / 2^5 / 2^4 / 2^3 / 2^2 / 2^1 / 2^0
------------------------------...

So your numbers are 257 and 431. OK - so lets look at the base 2 power items and notice that I made sure we went past your two numbers. So we know that 431 will start with 2^8 (closest number without goving over) and 257 will be 2^8 as well.

Let's covert first. 2^8/2^7/2^6/2^5/2^4/2^3/2^2/2^1/2^0

257 = 256 +0+0+0+0=0+0+0+1 so

we have one 2^8 and one 2^0 so the 257 = 100000001

Let's do 431

431 = 256+128+0+32+0+8+4+2+1 so

we have 110101111.

SO now lets add 100000001 + 110101111

It works like regular addition, except when you get a 2 you carry a one instead of when you get a 10.

So when we add we get
100000001
110101111
--------------------
1010110000

Now covert this back

1 2^9 = 512
1 2^7= 128
1 2^5 = 32
1 2^4 = 16

= 688 ! vola!

Hope this helps.

Answer 2

You are right about 688 = 1010110000

To add the numbers you just do it like normal addition, carrying a 1 if necessary (obviously it is binary so 1 + 1 = 0 carry 1)

11111
257 = 100000001
431 = 110101111
-----------------
1010110000

Answer 3

I had to refresh myself on this, but here's the scoop.
257 = 100000001 and 431 = 110101111
Recall that when you add two 1's you get a 0 but have to carry a 1 to the next column. So, you are correct in that
688 = 1010110000
Hope this clarifies it for you. Good luck.

Answer 4

I won't add to the above, but, are you aware that most modern computers have a built-in calculator, which, in "Scientific" (or similar) mode, can easily do binary math? Granted, it can't show you the work steps, but you could have verified your figures with it! Check out the link, below, too!

Answer 5

257d = 100000001
+
431d = 110101111
-------------------------------------

688d = 1010110000b