Binary Arithmetic
Overview
A processor cannot do arithmetic the way you were taught it at primary school, because it has no digits from 2 to 9 to work with. It has 0 and 1, and out of those two symbols and one rule about carrying it builds every sum, every difference, every price total and every frame of every game you have ever played. The surprising part is how small that rule is: binary addition has four cases, and you already know three of them.
This lesson teaches you to add two binary numbers by hand and to shift a binary number left or right, which is the trick a processor uses to multiply and divide by powers of two at almost no cost. You will also learn what gets thrown away when a shift runs off the end of an eight bit register, because knowing what a shift destroys is what separates a candidate who can perform one from a candidate who can be trusted to use one.
Objectives
- Be able to add together two binary numbers.
- Be able to apply a binary shift to a binary number.
- Describe situations where binary shifts can be used.
Mind map
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Binary Arithmetic. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- In binary addition, what is written down and what is carried when a column contains 1 + 1? A. Write 1, carry 0 B. Write 0, carry 1 C. Write 2, carry 0 D. Write 1, carry 1 Answer: B
- What is 00001100 + 00000110 in binary? A. 00010010 B. 00010100 C. 00001110 D. 00011000 Answer: A
- A logical left shift of 1 place has what effect on the denary value of a binary number? A. Halves it B. Doubles it C. Adds 1 to it D. Leaves it unchanged Answer: B
- The binary number 00011000 is given a logical right shift of 2 places. What is the result? A. 00000110 B. 01100000 C. 00001100 D. 00000011 Answer: A
- Which calculation can be carried out using a single binary shift? A. Multiply by 10 B. Multiply by 16 C. Multiply by 3 D. Multiply by 100 Answer: B
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