Exploring Binary and Hexadecimals

Luna is trying to convert the decimal number 10 into its binary equivalent. Can you help her?

• 1011

• 1001

• 1100

• 1010

Answer explanation

The binary equivalent of the decimal number 10 is 1010. This is derived by converting 10 into binary, where 10 in decimal equals 2^3 (8) + 2^1 (2) = 1010 in binary.

Mia is learning about computer memory and asks, 'How many bits are in a byte?'

• 32

• 4

• 16

• 8

Answer explanation

A byte consists of 8 bits. This is a standard unit of digital information storage, making 8 the correct answer among the choices provided.

During a coding class, Samuel is trying to convert the decimal number 255 into its hexadecimal representation. Can you help him?

• FF0

• FE

• F0

• FF

Answer explanation

The decimal number 255 converts to hexadecimal as follows: 255 divided by 16 gives 15 (F) with a remainder of 15 (F). Therefore, the hexadecimal representation is FF.

Jackson has a binary number 1011 and wants to convert it to decimal.

• 10

• 11

• 12

• 14

Answer explanation

To convert the binary number 1011 to decimal, calculate: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11. Thus, the correct answer is 11.

Kai has a binary number 1111 and wants to know its value in decimal. What is the value?

• 10

• 15

• 12

• 14

Answer explanation

The binary number 1111 is calculated as follows: 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 8 + 4 + 2 + 1 = 15. Therefore, the decimal value of 1111 is 15.

Hannah is trying to understand how to convert a hexadecimal number to binary for her computer science project. What is the correct method she should use?

• Add leading zeros to the hex number.

• Convert each hex digit to its decimal equivalent.

• Multiply each hex digit by 16.

• Replace each hex digit with its 4-bit binary equivalent.

Answer explanation

To convert a hexadecimal number to binary, replace each hex digit with its 4-bit binary equivalent. This method directly translates each digit, making it the most efficient and accurate way to perform the conversion.

David has two binary numbers, 1010 and 1101, and he wants to add them together. What is the result of his addition?

• 10111

• 1010

• 10001

• 1110

Answer explanation

To add the binary numbers 1010 (10 in decimal) and 1101 (13 in decimal), align them and add: 0+1=1, 1+0=1, 0+1=1, 1+1=10 (carry 1). This gives 10111 (23 in decimal), which is the correct answer.

Grace is learning about different number systems in her computer science class. What is the purpose of using hexadecimal in computing?

• To provide a more human-readable representation of binary data.

• To convert decimal numbers to binary.

• To represent colors in web design.

• To increase the speed of data processing.

Answer explanation

Hexadecimal is used in computing to provide a more human-readable representation of binary data. It simplifies the representation of binary numbers, making it easier for programmers to read and write code.

Oliver has a collection of 16 marbles and wants to organize them in a way that represents their quantity in hexadecimal.

• 14

• 20

• 1A

• 10

Answer explanation

To convert the decimal number 16 to hexadecimal, divide 16 by 16. The quotient is 1 and the remainder is 0. Thus, 16 in hexadecimal is represented as 10. Therefore, the correct answer is 10.

Jackson is trying to convert the hexadecimal number A3 into its binary representation. Can you help him?

• 10100011

• 11010011

• 10100010

• 10010011

Answer explanation

The hexadecimal number A3 converts to binary by converting each hex digit: A = 1010 and 3 = 0011. Combining these gives 10100011, which is the correct binary representation.