APCSP - Unit 1 Review

Here are three 4-bit binary numbers: 0010, 1010, and 0110. Which Base 10/decimal numbers is not equal to one of these?

• 9

• 10

• 6

• 2

Answer explanation

0010 -> 2

1010 -> 10

0110 -> 6

Remember, all binary numbers that end in 0 are even. All binary numbers that end in 1 are odd.

What is the minimum number of bits required to assign a unique value to 50 different things?

• 4

• 5

• 6

• 7

Answer explanation

Max 4 bit number is 15.

Max 5 bit number is 31.

Max 6 bit number is 63.

Max 7 bit number is 121.

Since we are looking for the MINIMUM number of bits required, the correct answer is 6.

Why does representing certain numbers (like irrational numbers or repeating decimals) cause loss of precision in binary?

• A fixed number of bits causes overflow errors

• An unlimited number of bits causes round-off errors

• It doesn't, you can represent any fractional number in binary

• A fixed number of bits causes round-off errors

Answer explanation

While it is true that a fixed number of bits can cause overflow errors, when we are talking specifically about loss of precision, that concerns round-of errors since you can't represent all fractional numbers using a fixed number of bits.

Moving from using 2 bits to 8 bits allows us to store 2^7 times as many values.

• True

• False

Answer explanation

Each additional bit doubles the amount of values we can store.

8 bits is 6 more than 2 bits. So that's doubling 6 times. 2x2x2x2x2x2 is 2 to the 6th power.

You can represent the the position of a light switch using a single binary digit.

• True

• False

Answer explanation

A single binary digit allows us to store one of two values. A light switch can either be on or off, so this is true.

What happens if I add two zeros to the end of a binary number? I.e. 110 -> 11000

• Its value is doubled

• Its value is tripled

• Its value is quadrupled (4x)

• Its value is octupled (8x)

Answer explanation

110 in binary is 6 in decimal.

11000 in binary is 24 in decimal.

24 is 4 times as much as 6.

Also, remember that each additional binary digit doubles the amount of values/information. 2 more digits -> 2x2 -> 2 squared -> 4 times as much.

What always happens when we sample analog information to represent it digitally?

• It is approximated at regular intervals and represented in bits

• The precision improves

• The quality improves

• It stays the same

You can represent the number of people in this class using only two binary digits

• True

• False

Answer explanation

The maximum two digit binary number is 11, which is 3 in decimal/base 10/the normal numeric system.

True or False: 8 bits makes 1 byte. The maximum decimal (base 10) value that can be represented by one byte is 256.

• True

• False

Answer explanation

It's true that 8 bits = 1 byte. It is also true that you can represent 256 total values with 1 byte.

HOWEVER - the maximum 8 bit number is 255 (decimal/base 10) since you have to include zero (0) in the values you can represent.

256 (decimal/base 10) is the first 9 bit number.

Which of these is the best definition of abstraction?

• Abstraction allows us to represent complex information or perform complex tasks by showing underlying complexity.

• Abstraction allows us to represent complex information or perform complex tasks by hiding underlying complexity.

• Programming in machine language (binary) instead of a programming language like JavaScript.

• None of these are a good definition.