CPEN111: Lecture 8 - Overflow

These flashcards cover key concepts about overflow, the 2's complement system, and floating point numbers as discussed in Lecture 9.

What is the 2's complement form used for in computing devices?

Binary addition and subtraction.

What is the largest possible value for a 2’s complement binary number with n bits?

2^(n-1) - 1 (0 followed by all 1s).

What does the arithmetic operation of adding 1 and 6 using 2’s complement yield?

The result is 7.

What indicates overflow when adding two positive numbers in 2’s complement?

If the sum yields a negative result.

In a 5-bit 2's complement system, what are the maximum and minimum values?

Max is +15 (01111) and min is -16 (10000).

What result do we get when adding -3 and -6 in 2’s complement?

The result is -9, correctly calculated as 1 0111.

What occurs after overflow when using 2's complement representation?

Wrap-around to the other end of the representable range.

How can we detect overflow during addition in binary?

If the carry into the most significant bit (MSB) differs from the carry out.

What are potential ways to handle overflow when detected?

Raise an error, saturate the result, or ignore the overflow.

What is ULP and why is it significant in numeric calculations?

Unit in the last place; it measures the accuracy of computations.

Why does ULP density vary in floating-point numbers?

Representable numbers are denser near zero and sparser farther away.

What trade-offs must be considered when using floating-point numbers to avoid overflow?

Hardware complexity, uncertainty in accuracy, and potential rounding errors.

What is the IEEE 754 standard?

Standard for floating-point arithmetic with specific formats for representation.

What does normalization mean in floating-point addition?

Adjusting the numbers to have the same exponent before adding them.

What error occurs when deriving ULP of a floating-point number?

Rounding error which quantifies how precise the representation is.

What does a carry out tell us in two's complement operations?

It does not inform about overflow.