Imagine that you are on an alien planet where one day is 8 hours long. If you look at a clock on this planet and see that it is 6 o’clock, what time will it be in 5 hours?
o’clock.
Hint.
Draw out the 8-hour clock and walk through the addition of each hour starting at 6.
Checkpoint4.5.2.Carry Out vs. Overflow.
When adding a positive and a negative number, which of the following is true:
There is never overflow
Correct!
There is always overflow.
Incorrect.
There may or may not be overflow.
Incorrect.
Checkpoint4.5.3.Modular Arithmetic and Binary Addition.
Given any two 8-bit unsigned values A and B, which of the following expressions represents the 8-bit result value of adding \(A+B\text{?}\)
\((A + B) \% 2^8\)
Correct!
\(A + B\)
Incorrect.
\((A + B) / 8\)
Incorrect.
\((A + B) // 2^8\)
Incorrect.
None of these options
Incorrect.
Checkpoint4.5.4.Overflow in Two’s Complement Addition.
When adding two 4-bit two’s complement values, there is overflow if:
the operands are 0xxx and 0xxx, and the result is 1xxx.
Correct!
the operands are 0xxx and 0xxx, and the result is 0xxx.
Incorrect.
the operands are 0xxx and 1xxx, and the result is 1xxx.
Incorrect.
the operands are 0xxx and 1xxx, and the result is 0xxx.
Incorrect.
the operands are 1xxx and 1xxx, and the result is 0xxx.
Correct!
the operands are 1xxx and 1xxx, and the result is 1xxx.
Incorrect.
Checkpoint4.5.5.Overflow in Two’s Complement Subtraction.
When subtracting two 4-bit two’s complement values, there is overflow if:
the calculation is 0xxx - 1xxx and the result is 1xxx.
Correct!
the calculation is 0xxx - 0xxx and the result is 1xxx.
Incorrect.
the calculation is 0xxx - 0xxx, and the result is 0xxx.
Incorrect.
the calculation is 0xxx - 1xxx and the result is 0xxx.
Incorrect.
the calculation is 1xxx - 0xxx and the result is 0xxx.
Correct!
the calculation is 1xxx - 0xxx and the result is 1xxx.
Incorrect.
the calculation is 1xxx - 1xxx and the result is 0xxx.
Incorrect.
the calculation is 1xxx - 1xxx and the result is 1xxx.
Incorrect.
Checkpoint4.5.6.Unsigned Overflow.
Will adding 7 and 5 together result in an overflow when using 4-bit unsigned binary representations?
No
Correct!
Yes
Incorrect.
Checkpoint4.5.7.Signed Overflow.
Will adding 7 and 5 together result in an overflow when using 4-bit signed binary representations?
Yes
Correct!
No
Incorrect.
Checkpoint4.5.8.Unsigned Overflow.
For which unsigned arithmetic operation will having a carry out result in an overflow?
Addition
Correct!
Subtraction
Incorrect.
Both A and B
Incorrect.
Neither A nor B
Incorrect.
Checkpoint4.5.9.Signed Overflow.
Given two N-bit two’s complement numbers, X and Y, where both have the same value for the most significant bit, which of the following statements are true?
Performing X+Y will sometimes lead to an overflow.
Correct!
Performing X-Y will never lead to an overflow.
Correct!
Performing X+Y will always lead to an overflow.
Incorrect.
Performing X+Y will never lead to an overflow.
Incorrect.
Performing X-Y will always lead to an overflow.
Incorrect.
Performing X-Y will sometimes lead to an overflow.
Incorrect.
Checkpoint4.5.10.Signed Overflow.
When adding two N-bit two’s complement numbers, X and Y, in which of the following scenarios might there be an overflow?. Select ALL that apply.
