Binary Addition Question??

Question

Why is 1 + 1 + 1 = 3??

my teacher explains this as 1+1+1 = 2^0+2^1,

why is this like this??

why isn't it 2^1+2^1+2^2??

I mean why isn't it 2^0 + 2^1 + 2^2??

Answer 1

I think your teacher is getting a bit muddled. 1+1+1 in binary = 11. This is 2^1 + 2^0. Binary can only have the digits 0 and 1. Decimal can have the digits 0,1,2,3,4,5,6,7,8,9 so 1+1+1=3.

Whatever base number you are using, there can only be the digits from 0 to one less than the base. So octal (base 8) uses 0,1,2,3,4,5,6,7 and hexadecimal (base 16, 2^4), the 'quick' way of writing binary, uses 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, F. Because hexadecimal is base 16, there has to be some way of representing the numbers beyond 9 and the convention is to use capital letters. A=10, B=11, C=12, D=13, E=14, F=15.

This bit is more advanced.
Whatever base you are using, a number is written in the form a*x^n + b*x^(n-1) + c*x^(n-2).....+ z*x^0,
where a,b,c,... are the figures as written, x is the base that you are writing in, and n, (n-1),...are the powers of the base. Eg 743 cannot be a number in binary, the lowest base it can be is octal because it has the figure 7.
In octal 743 represents 7*8^2+4*8^1+3*8^0=448+32+3=483 in dec
In decimal it represents 7*10^2+4*10^1+3*10^0
In hex it represents 7*16^2+4*16^1+3*16^0=1792+64+3 =1859 dec.

Answer 2

Because 1+1 = 2^0 + 2^0 = 2 * 2^0 = 2^1
1+1+1 = 2^0 + 1 + 1 = 2^0 + 2^1

Answer 3

Binary numbers are only 0 or 1. That means that you have 2 numbers. With computers, you always start with 0 so therefore it is 2^0 +2^1 = 3 or 1 +2 =3 2^0 is equal to 1 because 2/2 is 1.

This could help: http://en.wikipedia.org/wiki/Binary_numeral_system

Answer 4

the reason is because anything raised to the power of 0 is equal to 1 so 2^0 = 1.
therefore 1+1+1 = 2^0+2^1, because
2^0 = 1 and 2^1= 2
1+2=3.,

Answer 5

To begin with in binary numbers 1+1+1 = 11
11 in expanded form is 1*2^0+1*2^1 because the first place is always one's place and the only way you can get a one out of a 2 is to raise it to the zeroth power.

Your suggestion would add to 7

Answer 6

a million one 0 one 111 Make a table with columns having 2^0, 2^a million, 2^2, 2^3.... and so on. placed 2^0 interior the a great way actual column and then circulate left. Write the numbers under with a single digit in each and every column Then basically make any that have a one in the two columns a nil and carry a one in the time of to the subsequent (like in regularly occurring addition say once you get 2 5's). on the top, each and every column that has a 'a million' you upload the two^... words at the same time to transform returned to decimal occasion | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^a million | 2^0 | | a million | 0 | a million | a million | 0 | 0 | a million |+ | 0 | 0 | a million | 0 | a million | a million | 0 | ________________________________ =| a million | a million | 0 | a million | a million | a million | a million |

Answer 7

in binary 1+1= 01
01+1=11 which is binary for 3