Binary arithmetic and negative numbers

Overview

Rules for adding two binary digits, overflow in fixed-length binary addition and range of values an eight-bit two's complement store can hold.

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

   0 plus 0 gives 0, 0 plus 1 gives 1, 1 plus 0 gives 1, and 1 plus 1 gives 0 with a carry of 1 into the next column.

2. 2

   What is the result of adding three 1s in one column, as happens when a carry arrives?

   Model answer

   The result is 1 in that column with a carry of 1 into the next, because three in denary is 11 in binary.

3. 3

   Add 00110101 and 00010110 in binary and check the result in denary.

   Model answer

   The sum is 01001011, which is correct because the two values are 53 and 22 in denary and the result is 75.

4. 4

   Add 01101101 and 00010011 in binary and check the result in denary.

   Model answer

   The sum is 10000000, which is correct because the two values are 109 and 19 in denary and the result is 128.

5. 5

   What is overflow in fixed-length binary addition?

   Model answer

   Overflow is when the correct result needs more bits than the store provides, so the carry out of the leftmost column is lost and the value kept is wrong.

6. 6

   Does adding 00000001 to 11111111 in an eight-bit unsigned store overflow?

   Model answer

   Yes, because 255 plus 1 is 256 which needs nine bits, so the byte is left holding 00000000 with a carry lost off the end.

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