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1 + 1 = 0 in binary. Why does this happen?

Note: Adding binary numbers is related to modulo 2 arithmetic.

Let's review mod and modular arithmetic with addition.

modulus 2 is the mathematical term that is the remainder from the quotient of any term and 2. For instance, if we have 3 mod 2, then we have 3 / 2 = 1 + ½. The remainder is 1. So 3 ≡ 1 mod 2.

What if we want to add moduli?

The general form is a mod n + b mod n ≡ (a + b) mod n.

Now, for the given problem, 1 mod 2 + 1 mod 2 ≡ 2 mod 2. Then, 2 mod 2 ≡ 0 mod 2.

Therefore, 1 + 1 = 0 in binary.

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Q: Why does 1 plus 1 equals 0 in binary?
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Related questions

How would you write the number 37 in binary?

100101 1 times 2^0 = 1 PLUS 0 times 2^1 = 0 PLUS 1 times 2^2 = 4 PLUS 0 times 2^3 = 0 PLUS 0 times 2^4 = 0 PLUS 1 times 2^5 = 32 EQUALS 37


When is 1 plus 1 equals 10?

When you are working in binary arithmetic.


CAN 0 plus equals B plus equals B?

Yes because if 1+0=1 than 0 plus b equals b


What is 1 plus 1 plus 1 plus 1-4 plus g equals?

1 plus 1 plus 1 plus 1 equals 1 times 4. 1 times 4 equals 4. 4 minus 4 equals 0. 0


What is the binary solution to 101 plus 101?

( 1 0 1 ) + ( 1 0 1 ) = 1 0 1 0


What is 2 plus 1 plus 0 plus 1 plus 2 plus 1 plus 0 plus 0?

It equals 7


What decimal number is represents the binary number 10?

In binary this would be written as 1010. This is because in binary (from right to left) the digits in this number mean:(0 * 20) + (1 * 21) + (0 * 22) + (1 * 23).This is equal to (0 * 1) + (1 * 2) + (0 * 4) + (1 * 8), which equals 0 + 2 + 0 + 8, which equals 11 (in decimal).


What is 2 plus 1 plus 0 plus 1 plus 2 plus 0?

It equals 6


When does 1 plus 1 equals 10?

This will be in binary arithmetic, i.e. base 2 arithmetic.


When using the rule for subtracting binary numbers 1-1 equals what?

2


Can 1 plus 1 equals 0?

If it's 1 +-1 =0


What binary number is represented by the decimal number 11?

In binary this would be written as 1011. This is because in binary (from right to left) the digits in this number mean: (1 * 20) + (1 * 21) + (0 * 22) + (1 * 23). This, of course, is equal to (1 * 1) + (1 * 2) + (0 * 4) + (1 * 8), which equals 1 + 2 + 0 + 8, which equals 11 (in decimal).