I have a question about how the base 2 binary system works.
In base 2 (binary system), which equation is false?
A) 11+1=101 B)1x10=10 C)11x11=1001 D) 100/1=100 E) 1+1+1=11
If anyone does get the answer, could you explain thoroughly how you got it? Thank you very much!
When you see a number like
143 we associate 1 as being in the hundreds place, 4 in the tens and 3 in the ones or
base two uses two instead of ten.
so lets write 14 as base two
so lets list the powers of 2
fourteen could be written as
so 14 base two is 1110
I hope this helps.
First, for you, the calculator that comes with windows can convert between binary and decimal (in scientific mode, which can be enabled under the "view" toolbar) but be careful lest it becomes a crutch.
Now, there are any number of ways to do this, when I'm hazy I just convert to decimal and check.
Converting to decimal this becomes:
Clearly A is the false answer. You can simply get good at converting back and forth (just takes a little practice) then do them all this way.
Otherwise, you can try to do it all in binary like this:
A)11+1 = 1(1+1) = (1+1)0 = 100
B)1*x = x so 1*10=10
1's digit: 1+0 = 1
2's digit: 1+1 = 10 -> 0 with a 1 carried to the 4's digit
4's digit: 1+0+1 (the last 1 is brought up from the 2's digit) = 10-> 0 with a 1 carried to the 8's digit
8's digit: 0+1 (the 1 is brought up from the 4's digit)
so the answer is 1001
(here is a better explanation of binary multiplication than I provided http://meseec.ce.rit.edu/eecc341-win...-12-6-2001.pdf)
D)x/1 =1 so 100/1=100
E) 1+1+1 = 10 + 1 = 11
Personally, I find it simpler to convert to decimal for most operations, but there are times when there isn't any need.