Addition
Contents
Binary Addition
Binary is being able to add two numbers together but are represented in binary form, which consist of 1s and 0s
There are four possibilities when adding binary numbers, these possibilities are:
a total of 0 (0+0) put down 0 a total of 1 (1+0, 0+1 or 0+0+carried 1) put down 1 a total of 2 (1+1) put down 0, carry 1 a total of 3 (1+1+ carried 1) put down 1, carry 1
For example, solve 6+7 using binary addition:
First convert 6 and 7 from denary to binary using your preferred method
6 = 4+2+0 = 110 7 = 4+2+1 = 111
Then add them keeping in mind the 4 possibilities and add each digit together, starting on the right:
110 + 111
So:
0+1 = 1
1+1 = 0 carry 1
1+1+ carried 1 = 1 carry 1
1 + 0 = 1
so 110+111 = 1101. Converting this number back to denary gives us an answer of 13.
Another Example
Adding More Numbers Together
You could get 3 numbers to add however you wont be given a situation in which there are more than a total of 3.
For example:
101
101
011+
Which would = 1101
Adding Binary Numbers Into Denary
There are many ways to add two binary numbers together and get a denary value as the answer. The two main ways of doing are as follows: Method 1, Calculate the denary value of each binary number then add the two denary values together, you then should have the answer in denary. Or Method 2 which is just as simple. Add the two binary numbers together using 8-bit binary addition, then convert your binary answer into denary.
Example
01110100 + 00011111, Give the answer in denary.
Firstly, 01110100 can be converted into denary... 01110100 = 116.
Also, 00011111 when converted into denary is... 00011111 = 31.
116 + 31 = 147.
Another Example
01010110 + 11011001, Give the answer in denary.
Firstly, do 8-bit binary addition.
so:
01010110 + 01011001
= 10101111
Then convert 10101111 into denary:
so:
10101111 = 175
Final Example
78 + 01010110, Give the answer in denary.
Since the question wants the answer in denary, we will firstly convert the binary value into denary so that we can properly add them together.
So:
01010110 = 86
Then we will add the two denary values together
78 + 86 = 164
If the question wanted the answer in 8-bit binary we would instead, convert the denary number into its binary value. And then we would add the two values together.
So:
128 64 32 16 8 4 2 1 78 = 0 1 0 0 1 1 0 1 01001101 01001101 + 01010110 = 10100100 The answer is 10100100