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## What are binary calculations?

Binary addition and binary subtraction are methods of adding or subtracting binary values without having to convert them into denary.

## Overflow & Underflow Errors

Overflow and underflow errors occur when there is not enough space to accurately represent a binary number in the bits available.

## What is an overflow error?

An overflow error occurs when a binary value is too large to be stored in the bits available.

In technical terms, an overflow error occurs if a carry (remainder) is present on the most significant bit (MSB).

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The CPU then sets the overflow flag to true.

The most significant bit (MSB) is the largest bit (always the one furthest to the left) of a binary value (e.g. 128 for an 8 bit value).

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A flag is an alert signal. It is either on or off. The overflow flag is turned on by the CPU when an overflow occurs.

## What is an underflow error?

An underflow error occurs when a number is too small to be stored in the bits available. The value is too close to 0 to be accurately represented in binary.

## Questo's Questions

4.3 - Binary Calculations:

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1a. Describe the terms 'most significant bit' and 'flag'. [2]

1b. Using the terms from 1a, explain what an overflow error is. [2]

1c. Describe what is meant by an underflow error.  [2]

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2. Add together the following binary values. If an overflow error occurs you must state one has occurred.

• a. 010110012 and 010001012  [2]

• b. 110110112 and 010111012  [2]

• c. 001101102 and 011010112  [2]

• d. 110110112 and 010101112  [2]

• e. 011011012 and 110101102  [2]

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3. Subtract the following binary values; put the first value on top of the second value:

• a. 100110102 and 000110002 [2]

• b. 110110112 and 010111012 [2]

• c. 011101102 and 011010112 [2]

• d. 110110112 and 010101112 [2]

• e. 111011012 and 110101102 [2]