Big Idea 2

A certain programming language uses 4-bit binary sequences to represent nonnegative integers. For example, the binary sequence 0101 represents the corresponding decimal value 5. Using this programming language, a programmer attempts to add the decimal values 14 and 15 and assign the sum to the variable total. Which of the following best describes the result of this operation?

• The correct sum of 29 will be assigned to the variable total.

• An overflow error will occur because 4 bits is not large enough to represent either of the values 14 or 15.

• An overflow error will occur because 4 bits is not large enough to represent 29, the sum of 14 and 15.

• A round-off error will occur because the decimal values 14 and 15 are represented as approximations due to the fixed number of bits used to represent numbers.

A video game character can face toward one of four directions: north, south, east, and west. Each direction is stored in memory as a sequence of four bits. A new version of the game is created in which the character can face toward one of eight directions, adding northwest, northeast, southwest, and southeast to the original four possibilities. Which of the following statements is true about how the eight directions must be stored in memory?

• Four bits are not enough to store the eight directions. Five bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Eight bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Sixteen bits are needed for the new version of the game.

• Four bits are enough to store the eight directions.

Which of the following are true statements about the data that can be represented using binary sequences?

1. Binary sequences can be used to represent strings of characters.

2. Binary sequences can be used to represent colors.

3. Binary sequences can be used to represent audio recordings.

• I only

• I and II only

• II and III only

• I, II, and III

Consider the 4-bit binary numbers 0011, 0110, and 1111. Which of the following decimal values is NOT equal to one of these binary numbers?

• 3

• 6

• 9

• 15

The position of a runner in a race is a type of analog data. The runner’s position is tracked using sensors. Which of the following best describes how the position of the runner is represented digitally?

• The position of the runner is determined by calculating the time difference between the start and the end of the race and making an estimation based on the runner’s average speed.

• The position of the runner is measured and rounded to either 0 or 1 depending on whether the runner is closer to the starting line or closer to the finish line.

• The position of the runner is predicted using a model based on performance data captured from previous races.

• The position of the runner is sampled at regular intervals to approximate the real-word position, and a sequence of bits is used to represent each sample.

Consider the following numeric values.

• Binary 1011

• Binary 1101

• Decimal 5

• Decimal 12

Which of the following lists the values in order from least to greatest?

• Decimal 5, binary 1011, decimal 12, binary 1101

• Decimal 5, decimal 12, binary 1011, binary 1101

• Decimal 5, binary 1011, binary 1101, decimal 12

• Binary 1011, binary 1101, decimal 5, decimal 12

Which of the following is an advantage of a lossless compression algorithm over a lossy compression algorithm?

• A lossless compression algorithm can guarantee that compressed information is kept secure, while a lossy compression algorithm cannot.

• A lossless compression algorithm can guarantee reconstruction of original data, while a lossy compression algorithm cannot.

• A lossless compression algorithm typically allows for faster transmission speeds than does a lossy compression algorithm.

• A lossless compression algorithm typically provides a greater reduction in the number of bits stored or transmitted than does a lossy compression algorithm.

A user wants to save a data file on an online storage site. The user wants to reduce the size of the file, if possible, and wants to be able to completely restore the file to its original version. Which of the following actions best supports the user’s needs?

• Compressing the file using a lossless compression algorithm before uploading it

• Compressing the file using a lossy compression algorithm before uploading it

• Compressing the file using both lossy and lossless compression algorithms before uploading it

• Uploading the original file without using any compression algorithm

A researcher is analyzing data about students in a school district to determine whether there is a relationship between grade point average and number of absences. The researcher plans on compiling data from several sources to create a record for each student.

The researcher has access to a database with the following information about each student.

• Last name

• First name

• Grade level (9, 10, 11, or 12)

• Grade point average (on a 0.0 to 4.0 scale)

The researcher also has access to another database with the following information about each student.

• First name

• Last name

• Number of absences from school

• Number of late arrivals to school

Upon compiling the data, the researcher identifies a problem due to the fact that neither data source uses a unique ID number for each student. Which of the following best describes the problem caused by the lack of unique ID numbers?

• Students who have the same name may be confused with each other.

• Students who have the same grade point average may be confused with each other.

• Students who have the same grade level may be confused with each other.

• Students who have the same number of absences may be confused with each other.

A team of researchers wants to create a program to analyze the amount of pollution reported in roughly 3,000 counties across the United States. The program is intended to combine county data sets and then process the data. Which of the following is most likely to be a challenge in creating the program?

• A computer program cannot combine data from different files.

• Different counties may organize data in different ways.

• The number of counties is too large for the program to process.

• The total number of rows of data is too large for the program to process.