Relationship between truncation error e and bits b

Specify the relationship between truncation error e and the bits b for representing the decimal into the binary?

E

Expert

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For 2's complement representation, error because of the truncation for both the positive and negative values of x is 0>=xt-x>-2-b

Where, b refers to the number of bits and xt refers to the truncated value of x.

The equation holds good for both the sign magnitude, 1's complement if x>0. If x<0, then for the sign magnitude and for 1's complement truncation error attenuates.

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