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GCSE Computing Theory © gcsecomputing.net 1 GCSE Computing 2.14 Data Representation Binary Arithmetic

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Learning Objectives: 2 add two 8-bit binary integers explain overflow errors which may occur GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Decimal Arithmetic Rules 3 ADDdenarydenary sum = 7= = 15= 5 (carry 1) GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Adding Decimal Numbers Carry + GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Adding Decimal Numbers Carry + 1 GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Binary Arithmetic Rules 6 ADDdenarybinarybinary sum = 0= 00= = 1= 01= = 1= 01= = 2= 10= 0 (carry 1) = 3= 11= 1 (carry 1) GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Adding Binary Numbers Carry Decimal AdditionBinary Addition 1 GCSE Computing GCSE Computing Theory © gcsecomputing.net

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Adding Binary Numbers Carry Decimal AdditionBinary Addition 1 GCSE Computing 1 1 GCSE Computing Theory © gcsecomputing.net

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Overflow in Binary Number Addition Carry Decimal AdditionBinary Addition GCSE Computing If we only have 4 bits to store the result there would be no room for a carry, so it is lost and we get the wrong answer. When there isn’t enough room for a result, this is called an overflow and it produces an overflow error. GCSE Computing Theory © gcsecomputing.net

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