--- tags: 225-spr22, mth225, lt-quiz --- # Learning Target Quiz 2 :::info This quiz contains *new versions of questions* for **Learning Targets 1 and 2** and *new questions* for **Learning Targets 3 and 4**. * It's to your advantage to attempt as many problems as possible. But you *do not* need to attempt all the problems. Only attempt the ones you believe you are ready to take. * Do your work on separate pages with **each Learning Target on its own separate page**. *Please do not put multiple Learning Targets on the same page.* * Make sure to consult the [Standards for Assessments in MTH 225](/KoT83ezHRYO3DqPyXMMMag) document before starting on your work, so you're clear on what is expected and what constitutes a "successful" attempt. * When you are done: **Scan** each Learning Target to a clear, legible, black-and-white PDF and **upload the PDF** to the designated folder on Blackboard. Remember *do not just take a picture with your camera* --- use a scanning app to create a PDF, and upload the PDF. ::: ## Learning Target 1 :::warning I can represent an integer in base 2, 8, 10, and 16 including negative integers in base 2. ::: Do **all** of the following: 1. Convert the base 10 integer $167$ to binary. *Show your work and circle your answer*. 2. Convert the base 16 integer $55FA$ to decimal. *Show your work and circle your answer*. 3. Convert the base 2 integer 10011000 to octal. *Show your work and circle your answer*. 4. The 8-bit binary representation of the decimal number $121$ is 01111001. Write the 8-bit binary representation of $-121$ using two's complement notation. *Show your work and circle your answer*. **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. ## Learning Target 2 :::warning (**CORE**) I can add, subtract, multiply, and divide numbers in base 2. ::: Do **all** of the following: 1. Add the base-2 integers 11001011 and 10010110. *Show your work and circle your answer*. 2. Subtract the base-2 integers 11001011 and 10010110. *Show your work and circle your answer*. 3. Multiply the base-2 integers 10101 and 11. *Show your work and circle your answer*. 4. Divide the base-2 integer 11000110 by 10. *Show your work and circle your answer*. **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. ## Learning Target 3 :::warning (**CORE**) Given a conditional statement, I can state its hypothesis, conclusion, negation, converse, inverse, and contrapositive. ::: Consider the conditional statement: *If $n$ is even, then its binary representation ends in a 0.* 1. State the **hypothesis** of this statement. 2. State the **conclusion** of this statement. 3. State the **converse** of this statement. 4. State the **inverse** of this statement. 5. State the **contrapositive** of this statement. 6. State the **negation** of this statement (without simply putting "Not" or "It is not the case that" in the front of the statement). **Success criteria:** All answers are given in clear and correct English (*not* in symbolic notation). The negation and contrapositive must be correct, and no more than one error is allowed in the others. ## Learning Target 4 :::warning I can construct a truth table for propositions involving 2, 3, or 4 statements. ::: Construct a correct truth table for each of the following statements. 1. $\neg (p \wedge q)$ 2. $p \rightarrow (q \vee r)$ **Success criteria:** Both truth tables have the correct number of rows with no duplicated rows. All intermediate columns are shown. No more than three total errors are permitted. (If you make a mistake in an intermediate column but the rest of the row is correct given that mistake, then the mistake only counts once.)