# In Binary Arithmetic 1 + 1 = 10 ? Why Is This?

Can some please explain this? I've been searching online but I can't understand the explanations.

Bạn đang xem: In binary arithmetic 1 + 1 = 10 ? why is this? In base 10, 9+1 is 10 because after 9, there are no more symbols khổng lồ express a larger number, so it has lớn move over to the left and cycle back khổng lồ the beginning to mark that we've gone through one complete cycle in the 1's place.

In base 2 there are no more symbols khổng lồ express a larger number after '1', so the same thing happens. The number shifts over to lớn the left & the 1's place starts over.

Okay. So the only rules for binary addition are:

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 10

1 + 1 + 1 = 11

These are all I need lớn remember?

The ones column can only contain 0 or 1 in it in binary. (In contrast, the ones column in decimal notation can contain 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 in it.)

Once the ones column is filled up, you need to start using the twos column. (Just lượt thích 9 + 1 requires you to lớn move to lớn the tens column and write 10 in decimal.)

So if you have 1 in binary, và you add 1. You have to lớn express it as 10 but this means two.

That means:

1 * 21 + 0 * 20, i.e. "1 two plus 0 ones."

Just lượt thích in decimal notation 10 means

1 * 101 + 0 * 100, i.e. "1 ten plus 0 ones."

Similarly, when you need to địa chỉ cửa hàng 7 & 1 in binary it looks lượt thích this:

111 + 1 = 1000

seven is 111 = (1 * 22) + (1 * 21) + (1 * 20), i.e. "1 four plus 1 two plus 1 one."

one is 1 = (1 * 20), i.e. "1 one."

eight is 1000 = (1 * 23) + (0 * 22) + (0 * 21) + (0 * 20), i.e. "1 eight plus 0 fours plus 0 twos plus 0 ones."

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level 1

· 5 yr. Ago

In binary representation the last digit represents the amount of 20s, the second one the 21's, ..., the n'th one the 2n's. In the same way 298 in decimal means 8 units, 9 tens, 2 hundreds.

1 + 1 = 2, which is one 21 và zero 20's. (Note that đôi mươi = 1).

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So in binary that would be 10.

To check if you understand:

what is 5 in binary, what is 10 in binary representation?

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level 1

· 5 yr. Ago

Because that's what 10 means in binary.

In base 10 we have 10 total symbols, the digits 0,1,2,3,4,5,6,7,8,9. Khổng lồ represent larger numbers we have a positional system, so 10 just means one "ten" plus zero. 11 means one "ten" plus one. 55 means five "tens" plus five. 102 means "ten" squared plus two. 1002 means "ten" cubed plus two.

In base 9 we have 9 total symbols, the digits 0,1,2,3,4,5,6,7,8. To represent larger numbers we have a positional system, so 10 just means one "nine" plus zero. 11 means one "nine" plus one. 55 means five "nines" plus five. 102 means "nine" squared plus two. 1002 means "nine" cubed plus two.

In base 8 we have 8 total symbols, the digits 0,1,2,3,4,5,6,7. To lớn represent larger numbers we have a positional system, so 10 just means one "eight" plus zero. 11 means one "eight" plus one. 55 means five "eights" plus five. 102 means "eight" squared plus two. 1002 means "eight" cubed plus two.

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In base 5 we have 5 total symbols, the digits 0,1,2,3,4. To lớn represent larger numbers we have a positional system, so 10 just means one "five" plus zero. 11 means one "five" plus one. 55 doesn't mean anything because we don't have a symbol for five; five is the base so khổng lồ represent five you write 10. That means one "five" plus zero.