Number Base Systems

Sophia is learning about different number systems in her computer science class. What is the binary number system?

• The binary number system is a base-10 numeral system that uses digits 0-9.

• The binary number system is a hexadecimal system that uses digits 0-9 and A-F.

• The binary number system is a base-2 numeral system that uses only the digits 0 and 1.

• The binary number system is a base-2 numeral system that uses digits 1 and 2.

Answer explanation

The binary number system is a base-2 numeral system, meaning it uses only two digits: 0 and 1. This distinguishes it from base-10 (decimal) and hexadecimal systems, making the correct choice the one that accurately describes its structure.

Grace has a collection of 10 apples and wants to know how many apples she would have if she converted that number to binary.

• 1010

• 1001

• 1011

• 1100

Answer explanation

To convert the decimal number 10 to binary, divide by 2 and record the remainders. 10 ÷ 2 = 5 (remainder 0), 5 ÷ 2 = 2 (remainder 1), 2 ÷ 2 = 1 (remainder 0), 1 ÷ 2 = 0 (remainder 1). Reading the remainders from bottom to top gives 1010.

James is learning about different number systems in his computer science class. What is the hexadecimal number system?

• A base-10 system using symbols 0-9 only.

• A base-16 system using symbols 0-9 and A-E.

• A base-8 system using symbols 0-7.

• The hexadecimal number system is a base-16 system using symbols 0-9 and A-F.

Answer explanation

The hexadecimal number system is a base-16 system that uses the symbols 0-9 to represent values zero to nine and A-F to represent values ten to fifteen. Thus, the correct choice is that it uses symbols 0-9 and A-F.

David has a collection of 1010 marbles. How many marbles does he have in decimal?

• 9

• 11

• 8

• 10

Answer explanation

To convert the binary number 1010 to decimal, calculate: 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 8 + 0 + 2 + 0 = 10. Thus, the correct answer is 10.

James is learning about different number systems in his math class. What is the octal number system?

• The octal number system is a base-10 system using digits 0-9.

• The octal number system is a base-16 system using digits 0-F.

• The octal number system is a base-2 system using digits 0-1.

• The octal number system is a base-8 system using digits 0-7.

Answer explanation

The octal number system is a base-8 system, meaning it uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. This distinguishes it from other systems like decimal (base-10) and hexadecimal (base-16).

Abigail has 8 apples and wants to know how many apples she would have if she converted them into octal.

• 10

• 16

• 20

• 12

Answer explanation

To convert the decimal number 8 to octal, divide 8 by 8, which gives a quotient of 1 and a remainder of 0. Reading the quotient and remainder from top to bottom gives us 10 in octal. Thus, the correct answer is 10.

Benjamin is trying to explain the process of number base conversion to his classmates.

• Using only addition and subtraction for base conversion.

• Only converting numbers that are already in binary format.

• Converting directly from one base to another without using decimal.

• The process of number base conversion includes converting to decimal and then to the desired base.

Answer explanation

The correct choice explains that number base conversion typically involves converting a number to decimal first, as it simplifies the process, before converting it to the desired base. This method ensures accuracy in the conversion.

During a computer science class, Aria asked her classmates, "What is the binary equivalent of the decimal number 15?"

• 1001

• 1111

• 1110

• 1010

Answer explanation

The binary equivalent of the decimal number 15 is obtained by converting it to base 2. 15 in binary is represented as 1111, which corresponds to 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0.

Mia is learning about the binary number system in her computer science class. Can you list one application of the binary number system that she might find interesting?

• Data storage in hard drives

• Audio encoding in music files

• Color representation in graphics

• Data representation in computers

Answer explanation

The binary number system is fundamental for data representation in computers, as it uses two states (0 and 1) to encode all types of data, including numbers, text, and instructions, making it essential for computer operations.

Isla has a collection of colored beads, and she wants to convert the color code for one of her favorite beads, which is represented in hexadecimal as 1A, to its decimal equivalent. What is the decimal equivalent of the hexadecimal number 1A?

• 26

• 24

• 1B

• 30

Answer explanation

To convert the hexadecimal number 1A to decimal, multiply each digit by 16 raised to the power of its position: (1 * 16^1) + (10 * 16^0) = 16 + 10 = 26. Thus, the decimal equivalent is 26.