Binary addition, overflow and shifts

Overview

Rules for binary addition, worked 8-bit additions, overflow and its problems, logical left and right shifts, and arithmetic right shifts on negative numbers.

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 single binary digits.

   Model answer

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

2. 2

   Add the 8-bit binary numbers 00101101 and 00011011.

   Model answer

   The binary sum is 01001000. The denary check is 45 + 27 = 72.

3. 3

   Add the 8-bit binary numbers 01110110 and 00111001.

   Model answer

   The binary sum is 10101111. The denary check is 118 + 57 = 175.

4. 4

   What is overflow?

   Model answer

   Overflow happens when the result of a calculation needs more bits than are available to store it. The extra bit is lost, so the stored result is wrong.

5. 5

   What is stored when 11001000 and 01100100 are added in an 8-bit register?

   Model answer

   The register stores 00101100, which is 44. The true sum is 100101100, or 300, which needs 9 bits, so the leading 1 overflows.

6. 6

   How can you spot that overflow has happened when adding two 8-bit unsigned numbers?

   Model answer

   Overflow has happened if a carry comes out of the most significant bit. The true answer would need a ninth bit.

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