How To Add and Subtract Binary Numbers | Computer Science

Summary

This video explains the basic operations of binary arithmetic, including addition, subtraction, multiplication, and division. It begins with simple concepts like adding 0+0 and 1+0, progressing to more complex rules, such as carrying over when adding binary numbers. Through multiple examples, the video demonstrates how to add and subtract binary numbers, explaining key principles like carrying over and borrowing. The video also includes tips on converting binary numbers to their decimal equivalents to verify answers, providing viewers with a thorough understanding of binary math.

Takeaways

• 😀 Adding binary numbers involves simple rules: 0 + 0 = 0, 1 + 0 = 1, and 1 + 1 = 0 with a carry of 1.
• 😀 When adding three 1s, the result is 1 with a carry of 1 to the next column.
• 😀 Binary addition follows column-by-column calculation, carrying over when necessary.
• 😀 Convert binary numbers to decimal to verify the accuracy of the result.
• 😀 In binary addition, carrying over changes a 1 + 1 result to 0, but requires adding 1 to the next column.
• 😀 Subtraction of binary numbers also involves borrowing, similar to decimal subtraction.
• 😀 When subtracting and encountering 0 - 1, borrow from the next column to avoid negative results.
• 😀 Each column in binary math represents a power of 2, such as 1, 2, 4, 8, etc.
• 😀 For binary subtraction, if the result of a column is negative, borrow from the next column that has a 1.
• 😀 Always check binary addition and subtraction by converting the result back to decimal to confirm accuracy.
• 😀 Practice with examples will help solidify the understanding of binary addition and subtraction techniques.

Q & A

What is the result of adding '0' and '0' in binary?

The result is '0', since 0 + 0 equals 0 in binary.

What is the sum of '1' and '0' in binary?

The sum is '1', because 1 + 0 equals 1 in binary.

When adding two '1's in binary, what do you get?

The sum is '0', with a carry-over of '1'. This is because 1 + 1 equals 2 in decimal, which is represented as '10' in binary.

How do you handle the addition of three '1's in a column in binary?

When adding three '1's in a column, the result is '1' with a carry-over of '1', producing a '1' in the result and carrying over another '1' to the next column.

What is the binary sum of 1010 and 1001?

The binary sum of 1010 and 1001 is 10011. You add the numbers column by column, carrying over when necessary.

What is the decimal equivalent of the binary number 1010?

The decimal equivalent of the binary number 1010 is 10. This is calculated by adding the values corresponding to the '1's in the binary places: 8 + 2.

In binary addition, what happens when you add '1' and '1' in the leftmost column and need to carry over?

When adding '1' and '1' in the leftmost column, the result is '0' and you carry over a '1' to the next column. This follows the rule of binary addition where 1 + 1 equals 10 in binary.

What is the decimal equivalent of the binary number 111001?

The decimal equivalent of the binary number 111001 is 57. This is calculated by adding the values of the binary places that have '1': 32 + 16 + 8 + 1.

How do you subtract '1' from '0' in binary?

To subtract '1' from '0' in binary, you need to borrow from the next higher column. This turns the '0' into a '2' (representing binary 10), and then subtracting 1 from 2 gives '1'.

What steps are involved in subtracting the binary number 100 from 1?

To subtract 1 from 100 in binary, you need to borrow as you can't subtract 1 from 0 in the first column. After borrowing, the result is '011' in binary, which is 3 in decimal.