Digital Information

The Apple iPhone includes a settings menu where you can toggle various accessibility options on or off。

What is the minimum number of bits that can represent those 2 options?

• 1

• 0

• 2

• 4

You're playing around with an old computer that only accepts binary numbers as input.

How would you enter the decimal number 73 into the old computer?

Type the binary number without any spaces:

When writing binary data, we often put a space between each byte to make it easier for humans to read.

Consider this binary data:

1011011010110001

Which option puts a space after each byte?

• 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1

• 1011 0110 1011 0001

• 1011011010110001

• 10110110 10110001

Which of these values can be stored in a single bit?

• 0

• 1

• 11

• 2

Which of these lists correctly orders the binary numbers from smallest to largest?

• 0001,0010,0110,0011

• 0100,0001,0111,0110

• 0011,0100,0111,1000

• 0011,0100,1000,0111

The video sharing site YouTube originally stored the number of video views in a 32-bit signed integer.

Then the viral hit "Gangnam Style" received more than 2,147,483,647 views (more than any other video at that time), and YouTube could not display an accurate number of views until they changed their code.

What is the best explanation of what happened?

• Limited precision of floating-point numbers

• Integer overflow error

• Incorrect use of integer instead of floating-point representation

• Round-off error in floating-point arithmetic

Consider a computer that uses 4 bits to represent positive integers and uses all 4 bits to represent the value.

Which of the following operations would results in integer overflow?

• 0100*0011

• 1000*0010

• 4*4

• 3+12

Ernesto writes this code to calculate the final cost of a meal with a tip of 20%:

meal ← 9.70

withTip ← 1.20

total ← meal * withTip

They're surprised to see that total stores the value 11.639999999999999 instead of 11.64.

What is the best explanation for that result?

• The result was too large of a number to be stored in floating-point representation.

• An integer overflow error occurred.

• The computer stored the result with floating-point representation instead of integer representation.

• The arithmetic operations on floating-point numbers resulted in a round-off error.

A civil engineer is writing code to calculate the center of gravity for a semi-ellipse:

radius ← 33.27

centerY ← (4 radius) / 3 PI

The code relies on the built-in constant PI. After running the code, centerY stores 14.120226551112957.

Their colleague checks the result by running the same calculation on their own computer. Their program results in a centerY of 14.120226551112925.

The two values are very close, but not quite the same.

Which of these is the most likely explanation for the difference?

• One of the computers experienced an integer overflow error when calculating the result.

• The two computers executed the arithmetic operations using a different order of operations.

• The two computers represent the constant PI with a different level of precision, due to their rounding strategy or size limitations.

• One computer used an integer representation for the numbers while the other computer used the more accurate floating-point representation.

VSCII a character encoding scheme developed in the 1990s in order to encode text written in Vietnamese. VSCII uses one byte to encode each character.

This binary data is a VSCII encoding of a single Vietnamese word:

1010111010111

How many characters are encoded in that binary data?

• 1

• 2

• 8

• 16