Unit 6 · Lesson 4
5 steps. Each one is a short story and a question to answer.
Adding and subtracting binary numbers works just like the decimal way you learned in primary school.
We work column by column, starting from the right (the lowest place) and moving left.
The only difference: binary has just two digits (0 and 1), so the rules are specific to them.
In addition we use a carry, in subtraction we use a borrow.
We start binary addition from...
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Column by column from the right: carry in addition, borrow in subtraction. We work column by column, starting from the right (the lowest place) and moving left. The only difference: binary has just two digits (0 and 1), so the rules are specific to them.
1 + 1 = 10 (write 0, carry 1) and 1 + 1 + 1 = 11 (write 1, carry 1). 0 + 0 = 0 and 0 + 1 = 1. 1 + 1 = 10: we write 0 and carry 1 to the next column, because the sum reached 2.
0101 + 1001 = 1110. First column: 1 + 1 = 10, write 0, carry 1. Second: 0 + 0 + carried 1 = 1. Third: 1 + 0 = 1.
When the top digit is too small: borrow 1 from the next column to make 10. 0 − 0 = 0, 1 − 0 = 1 and 1 − 1 = 0. When the top digit is too small (like 0 − 1), we borrow 1 from the next column, which turns into 10, worth 2.
1010 − 0110 = 0100 (we borrowed from the fourth column). First: 0 − 0 = 0. Second: 1 − 1 = 0. No borrowing. Third: 0 − 1 is impossible, so borrow 1 from the fourth to get 10, and 10 − 1 = 1.
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Every idea in the lesson with its rule, ready to screenshot and revise from.
Column by column from the right: carry in addition, borrow in subtraction
1 + 1 = 10 (write 0, carry 1) and 1 + 1 + 1 = 11 (write 1, carry 1)
0101 + 1001 = 1110
When the top digit is too small: borrow 1 from the next column to make 10
1010 − 0110 = 0100 (we borrowed from the fourth column)
One question from every step. Answer and see your score.
Question 1 of 5
We start binary addition from...
Unit 6
Learn how a computer adds and subtracts binary numbers: the addition rules and carry, the subtraction rules and borrow, with worked examples step by step, in an animated explainer.
The same explanation as the 3D scene, written out for quick review.
Column by column from the right: carry in addition, borrow in subtraction. We work column by column, starting from the right (the lowest place) and moving left. The only difference: binary has just two digits (0 and 1), so the rules are specific to them.
Page 116, 119
1 + 1 = 10 (write 0, carry 1) and 1 + 1 + 1 = 11 (write 1, carry 1). 0 + 0 = 0 and 0 + 1 = 1. 1 + 1 = 10: we write 0 and carry 1 to the next column, because the sum reached 2.
Page 116, 119
0101 + 1001 = 1110. First column: 1 + 1 = 10, write 0, carry 1. Second: 0 + 0 + carried 1 = 1. Third: 1 + 0 = 1.
Page 116
When the top digit is too small: borrow 1 from the next column to make 10. 0 − 0 = 0, 1 − 0 = 1 and 1 − 1 = 0. When the top digit is too small (like 0 − 1), we borrow 1 from the next column, which turns into 10, worth 2.
Page 117, 119
1010 − 0110 = 0100 (we borrowed from the fourth column). First: 0 − 0 = 0. Second: 1 − 1 = 0. No borrowing. Third: 0 − 1 is impossible, so borrow 1 from the fourth to get 10, and 10 − 1 = 1.
Page 117