Unit 1 Digital Information

Which of the following best describes how computing devices represent information?

• A computer will either represent information as bits or bytes but not both

• A computer represents data as a byte which is either a 0 or a 1

• A computer represents data as bits which is either a 0 or a 1

• A computer represents information as bits which contain 8 bytes.

Answer explanation

The definition of a bit: a contraction of "Binary Digit"; the single unit of information in a computer, typically represented as a 0 or 1.

Which of the following is NOT true of how computers represent complex information?

• Computing devices use patterns of bits to represent complex information

• Abstraction helps represent complex information by surfacing complexity that might otherwise be hidden

• Depending on context the same sequence of bits may represent different types of information

• Common abstractions that are represented by computing devices include numbers, characters, and color.

Answer explanation

Abstraction helps by hiding complexity rather than surfacing it. For example, you don't have to know all the details about how a car works in order to operate it.

When visiting a museum Lian takes a photo of a painting with a smartphone which stores the photo as an image file. Which of the following best describes the differences between the painting itself and the photo of the painting stored on the smartphone?

• Both the painting and the photo are analog

• The photo is a digital representation of the analog painting

• Sampling can be used to determine whether the analog image is an accurate representation of the painting

• The phone can represent the photo in either digital or analog formats depending on the sampling technique that is used

Answer explanation

A painting is an analog because it's something with continuous representation. A digital photo changes discreetly at every pixel using a finite set of colors.

Your computer uses 4 bits to represent decimal numbers (0, 1, 2, 3 and so on) in binary. What is the SMALLEST number for which an overflow error occur?

• 14

• 15

• 16

• 17

Answer explanation

The 4-bit binary number 1111 represents the decimal number 15. Counting up to the next number, 16, will cause the 4-bit binary number to overflow to 0000 just like an odometer.

Which of the following is true of how computers represent numbers?

• Using a fixed but large number of bits can eliminate the possibility of round off error when representing numbers in binary

• With a fixed number of bits some numbers are too large to represent in a computer which will lead to overflow errors.

• Using a fixed but large number of bits, for example 128, eliminates the possibility of overflow errors.

• With a large but fixed number of bits it is possible to eliminate either round-off errors or overflow errors, but not both.

Answer explanation

With a fixed amount of bits, no matter how many, at some point the largest possible value will be reached, with 1s for all the bits. Representing the next largest number will lead to an overflow error and the odometer will start back at all 0s.

Convert the binary (base-2) number 1001 to decimal (base-10).

• 9

• 10

• 16

• 17

Convert the decimal (base-10) number 20 to binary (base-2).

• 10010

• 00101

• 11000

• 10100

Answer explanation

Using your Flippy Do, the first place value that fits into 20, going from left to right, is 16, so the 16s place becomes a 1. Next, 4 remains and so you put a 1 in the 4s place. (1 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (0 x 1) = 20

Which of the following binary (base-2) numbers is LARGEST?

• 11000000

• 01111111

• 00000001

• 10111111

Answer explanation

Since all of these are 8-bit binary digits, the leftmost place value is the 128s place. 11000000 and 10111111 both have a 1 in the 128s place. Since 11000000 has a 1 in the 64s place and 10111111 does not, 11000000 is larger no matter the rest of the digits.

How many total numbers can be represented with an 8-bit binary (base-2) system?

• 127

• 128

• 255

• 256

Answer explanation

Binary is a base 2 number system. With each new bit, we double the amount of unique numbers we can make. With 7 bits, we can make the decimal numbers 0 to 127 (0000000 to 1111111), for a total of 128 unique numbers. When we go up to 8 bits, we can make the decimal numbers 0 to 255 (00000000 to 11111111) for a total of 256 unique numbers.

Which of the following is true of lossy and lossless compression algorithms?

• Lossy compression algorithms are used when perfect reconstruction of the original data is important.

• Lossy compression algorithms are typically better than lossless compression algorithms at reducing the number of bits needed to represent a piece of data.

• Lossless compression algorithms are only used to compress text data.

• Lossless compression algorithms only allow for an approximate reconstruction of the original data.

Answer explanation

Since lossless compression keeps all the information from the original item, it cannot do as good a job of reducing the number of bits as lossy compression where some of the original information is lost.