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Binary addition and subtraction —

Intro

This is a continuation of the learning binary series. Be sure to read learning binary before reading this post.

Binary addition

Lets start with basic decimal addition.
The basic values column
1000 | 100 | 10 | 1
Example

1 1
1 5 9 5
+ 3 5 6 4
_ _ _ _
5 1 5 9

We take the first digit and carry that. While the second digit remains below.
The digit you carried is added to the number.
5 + 4 = 9 > 9 Is less then 10 so we don’t carry over.
9 + 5 = 15 > 15 is higher then 10. We need to carry a 1 over into the 100’s column.
1 + 5 + 5 = 11 > 11 is higher then 10. We need to carry a 1 over into the 1000’s column.
1 + 1 + 3 = 5 > 5 is less then 10 so we don’t carry over.

Answer 5159

Onto binary addition
Binary addition is the same concept. Except for your using binary numbers 1 and 0.

The five basic addition rules

0 + 0 = 0
1 + 0 = 1
10 + 0 = 10
1 + 1 = 10 > 1 + 1 = 2 > 10 = 2 in binary
10 + 1 = 11

Example

1 1 1
1 0 1 1
+ 1 0 1 1
_ _ _ _ _
1  0  1 1 0

1 + 1 = 10 > We carry the 1
1 + 1 + 1 = 10 + 1 = 11 > We carry the 1
1 + 0 = 1
1 + 1 = 10 > Since there is no more columns to carry. We put 10.

You can double check

1011 = 11
1011 = 11
11 + 11 = 22
Answer 10110 = 22

 

Binary subtraction

Lets start with basic decimal subtraction

Example

 3  4 16 
3  3  5  6 4
2  3  4  9 0
_ _ _ _ _ _
1 0 0  7 4

4 – 0 = 4
Borrow 1 to make 16 – 9 = 7
Borrow to make 4 – 4 = 0
Borrow to make 3 – 3 = 0
3 – 2 = 1

Answer
 10074

Onto binary subtraction

The four basic subtraction rules

0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
10 – 1 = 1

 0 10   10
1  0  1   0 1
 1  1   1 0
_ _ _ _ _ _
0 0 1   1 1

1 – 0 = 1
Borrow 1 to make 10 – 1 = 1
Borrow 1 to make 10 – 1 = 1
Borrow 1 to make 1 – 1 = 0
Borrow 0 to make 0

You can double check

10101 = 21
1110 = 14
21 – 14 = 7
Answer 111 = 7

I hope you enjoy my tutorial on how to subtract and add binary numbers. The next guide in this series will be how to multiply and divide binary numbers.

 
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Categorised as: Binary


2 Comments

  1. Domenica says:

    If I saw this post back in October when I had to learn assembly code this would have been amazing helpful. The professor over complicated things. I am bookmarking this for future reference!

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