Binary addition, overflow and binary shifts

Overview

The rules for binary addition, worked additions, overflow errors and how to spot them, and left and right shifts with their effect as multiplication and division.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State the rules for adding binary digits.

   Model answer

   The sum 0 + 0 is 0, and 0 + 1 is 1. The sum 1 + 1 is 0 carry 1. The sum 1 + 1 + 1 is 1 carry 1.

2. 2

   Add the binary numbers 01011010 and 00110111.

   Model answer

   The total is 10010001. The denary check is 90 + 55 = 145.

3. 3

   Add the binary numbers 01101100 and 00101011.

   Model answer

   The total is 10010111. The denary check is 108 + 43 = 151.

4. 4

   What is an overflow error in binary addition?

   Model answer

   An overflow error happens when a result needs more bits than are available to store it. A total above 255 cannot fit in 8 bits.

5. 5

   Add 11001000 and 01100100, and explain what happens when the result is stored in 8 bits.

   Model answer

   The full total is 100101100, which needs 9 bits. The 9th bit is lost, so the stored result is 00101100, which is 44 instead of 300.

6. 6

   How can you tell that an 8-bit binary addition has overflowed?

   Model answer

   A 1 is carried out of the most significant bit column. The true total is then larger than 255.

Other ways to work this

The same content, four other ways.

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Six ways to work the same material.