The following are the steps for addition, subtraction, division, and multiplication of binary numbers.

Addition is much like solving decimal addition problems. Add each row of digits from right to left.
```Example1:          Example2:
101101110           10111110
+ 1011010          + 1011110
_________          _________
111001000          100011100
```

With addition, there are four important rules to remember. These four rules will help you solve any binary addition problem you will face:

• 0 + 0 = 0
• 1 + 0 = 1
• 1 + 1 = 0, plus 1 carry (carry over to the next number)
• Carry + 1 + 1 = 1, plus 1 carry

Subtraction of Binary Numbers:

```Example1:          Example2:
º¹ º¹               º¹¹ º¹
10110              1100110
-01101             -1011001
______             ________
1001                 1101
```

Like decimal subtraction, it is often required to borrow from the next digit. ¹ equals a borrow of one, and º equals a change as a result of the borrow.

Multiplication of Binary Numbers:

```Example1:          Example2:
1100100             10110111
x 01011             x 111111
_______             ________
1100100             10110111
11001000            101101110
000000000           1011011100
1100100000          10110111000
00000000000         101101110000
___________        1011011100000
01101001100        _____________
10110100001001
```

Know your 1 and 0 times tables? Then the rest is easy. Simply multiply each top number by the first digit in the multiplier. Be sure to remember your place holders; omitting them will screw up the answer. Then, once you have your big mess of ones and zeroes, add them together with the addition techniques above.

Division of Binary Numbers:

```Example1:          Example2:

10101.1              10110
_________           __________
10 | 101011.0      101 | 1101110
-10                  101
010                  111
-10                  101
011                 101
-10                 101
10                  00
10
0
```

Long division is the most efficient approach here. This will require lots of subtraction, so learn from the lesson above. Divide the number into the first number, subtract it underneath the quotient, drop the next digit down to the answer, and divide the dividend into that number. Repeat these steps until you can work no longer.