[CS] Paper 2/1-Data Representation/1.3-Binary Arithmetic

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  • Created by: 16tgc05
  • Created on: 16-10-21 13:48
What are the rules of binary addition ?
What is an overflow error ?
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0 carry 1
1 + 1 + 1 = 1 carry 1
An overflow error is where a calculation produces more bits than can be stored.
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What is the formula for working out the range of two's complement ?
Highest Number = 2**(n - 1)= result - 1
Lowest Number = -2**(n - 1) = result
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How would a fixed point table look with 8 bits in total with and 4 bits after the decimal point ?
8|4|2|1|0.5(1/2)|0.25(1/4)|0.125(1/8)| 0.0625(1/16)|
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How do you calculate the 'absolute error' ?
How do you calculate the 'relative error' ?
Absolute error : the difference between the number to be represented and the closet possible binary number. For example, 0.76 - 0.7578125

Relative error : the absolute error divided by the number to be represented. For example, 0.0021875 / 0.76 = 0.2876%
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What is the difference between an
'underflow error' and an 'overflow error' ?
An underflow error occurs when the number is too small to be represented in the given number of bits.

An overflow error occurs when the number is too large to be represented in the given number
of bits.
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Other cards in this set

Card 2

Front

What is the formula for working out the range of two's complement ?

Back

Highest Number = 2**(n - 1)= result - 1
Lowest Number = -2**(n - 1) = result

Card 3

Front

How would a fixed point table look with 8 bits in total with and 4 bits after the decimal point ?

Back

Preview of the front of card 3

Card 4

Front

How do you calculate the 'absolute error' ?
How do you calculate the 'relative error' ?

Back

Preview of the front of card 4

Card 5

Front

What is the difference between an
'underflow error' and an 'overflow error' ?

Back

Preview of the front of card 5

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