---
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.)