Binary addition and binary shifts

Overview

The rules for adding binary digits, worked additions of two and three numbers, overflow beyond 255, and left and right logical shifts as multiplication and division by powers of two.

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 two binary digits.

   Model answer

   The sum 0 + 0 is 0, and 0 + 1 is 1. The sum 1 + 1 is 10, so write 0 and carry 1.

2. 2

   What is 1 + 1 + 1 in binary, and how is it written in a column addition?

   Model answer

   The sum is 11 in binary, which is 3 in decimal. The column shows 1 and a 1 is carried to the next column.

3. 3

   Add the binary numbers 00101101 and 00011010.

   Model answer

   The total is 01000111. As a check, 45 + 26 = 71 in decimal, and 01000111 is 71.

4. 4

   Add the binary numbers 01010110 and 00111011.

   Model answer

   The total is 10010001. As a check, 86 + 59 = 145 in decimal, and 10010001 is 145.

5. 5

   Add the three binary numbers 00010101, 00100110 and 00001011.

   Model answer

   The total is 01000110. As a check, 21 + 38 + 11 = 70 in decimal, and 01000110 is 70.

6. 6

   How can you check the answer to a binary addition?

   Model answer

   Convert each number to decimal and add them. The decimal total should match the binary answer converted to decimal.

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