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