If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Algebra (all content)

### Course: Algebra (all content)>Unit 1

Lesson 14: Binary and hexadecimal number systems

When we add two numbers in binary, the key is that we can only use the digits zero and one. When we add two ones together, the result is two, but we have to write it as "10" in binary. Sometimes we have to "carry" a one over just like in regular addition.

## Want to join the conversation?

• Did anyone else get kind of confused when Sal added 1 + 1 in the one's place, to get 2 and then carried that 2 into the 2's column by adding another 1, making 1 + 1 + 1, which he then added to get"3", which he ""carried" by writing 3 as 11? I was thinking that having 3 ones in the 2's column would be added as 2 + 2 + 2 = 6, which equals 1 in the 4's place and 1 in the 2's place. You get the same answer (6 = 11, in terms of 4's and 2's), but it just seemed kind of confusing to me the way he did it.
• He converted the decimal 2 to the binary 10 and then carried the one. In the 2's column he added three 1's to get the decimal 3 which is binary 11. He again carried the 1 from 11 to the 4's column. Keep adding this way by carrying digits in binary the same way you did in decimal.
• Is there actually subtraction within binaries?
• Yes, like addition, it's the same as with decimal, only just using the numbers 0 and 1.

For 1011 - 111, you would start with the rightmost digits and do 1 - 1 =0. Then 1 -1 =0 for the second digit. For the third digit, you have 0 - 1, which you can't do, so you have to borrow a 1 from the forth digit to get 10 - 1, which is 1 (it's the equivalent of 2 - 1 = 1). So the final answer is 100. 1011 - 111 = 100, and indeed, 11 - 7 = 4.
• Then what if i add 101 + 111 + 101 + 111 = ? 4 in binary is what number?
• I wanted to understand how the borrow works when there is nothing ot borrow . Say I want to subtract 0110 from 1000 (1000 - 0110) .

First Step : 0 - 0 = 0 : This is fine.
Next : 0 - 1 = carry from next digit ,it is a 0 so carrry from next .So 10 - 1 = 1 . This is also fine.

But now what next since there is nothing to borrow and we are left with 0 - 1 .

Can some explain?
(1 vote)
• See you get a nine over there so convert 9 to decimal and solve . just do it like decimal borrowing
(1 vote)
• how do I solve this 00101110 + 11010111 = I got 100000101 is that right?
• When he said 1 +2 + 4 = 7 in binary, how did he get 7? Can someone please help me?Thank you
• Well, he got the 1, 2, and 4 from the place values of the number. Remember, in binary, the place values go: ones, twos, fours, eights, sixteens, etc. Thus, as there was ONE ones, ONE twos, and ONE fours, he go t the resulting 1,2,4. Then, if he simply adds these numbers, he should get the original decimal number, which is 7. Not sure if I explained this super well, but I think that is the basic idea.
(1 vote)
• Can someone explain me how he got the decimal numbers at the end?
for example 1011 stands for 1+2+4 = 7 (dec)
• A easy way to understand addition is also considering this
1+0 =0
0+1 = 0
1+1 = 10
1+10 = 11
11+1=100
100+1 = 101
101+1 = 110
110+1 = 111
111 + 1 = 1000
and so on.
(1 vote)
• Thank you! This is helpful, and 4 in binary is what nummber?