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Physics Lesson 17.1.4 - Binary Arithmetic
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Welcome to our Physics lesson on Binary Arithmetic, this is the fourth lesson of our suite of physics lessons covering the topic of Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Binary Arithmetic
We can do the four basic operations (addition, subtraction, multiplication and division) in the binary system in the same way as we them do in the decimal system. The only difference is that in addition, the value of the digit on the left increases by 1 when the value on its right becomes 2 (like in decimal system in which the value of the digit on the left increases by 1 when the place value on its right becomes 10). On the other hand, in subtraction we borrow 2 instead of 10 from the place value on the right to make the subtraction when this is impossible. Let's consider a couple of examples in this regard.
Example 1
Do the following operations:
- (11000101)2 + (01111010)2
- (11001100)2 + (00111001)2
Solution 1
We can write the numbers in columns to make the operations easier. Thus, we have:
In multiplication, we can use the same procedure as used in the decimal system as well. Putting the numbers in column is very helpful. For example, if we have to multiply (1101)2 and (101)2, we get
If you are in doubt about the correctness of your result, you can quickly convert the numbers in base 10 numbers and do the multiplication. This can be used as a proof for your work. Thus, (1101)2 = 8 + 4 + 1 = (13)10 and (101)2 = 4 + 1 = (5)10. Therefore, we have 13 × 5 = 65 for the product. Let's check whether (1000001)2 = (65)10. We have
= 64 + 1
= 65
Therefore, the result obtained by the binary multiplication is correct.
As for the division of binary numbers, we use the same procedure as in decimal system. For example, we known that 12 ÷ 4 = 3. When this division is done in the binary system, we obtain:
Thus, we obtained (1100)2 ÷ (100)2 = (11)2
We can also express the decimal numbers written in base 10 number system using the decimal place to divide the whole and the non-whole part of the number. For example, the binary number 11010.101 corresponds to
= 16 + 8 + 2 + 1/2 + 1/8
= 26 + 4 + 1/8
= 26 5/8
= 26.625
in the decimal system. Obviously, not all decimal numbers can be converted into binary ones; they must be powers of 2 to do this.
You have reached the end of Physics lesson 17.1.4 Binary Arithmetic. There are 5 lessons in this physics tutorial covering Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates, you can access all the lessons from this tutorial below.
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