GCSE Number Systems

Which of the following number systems is base-2?

• Decimal

• Hexadecimal

• Binary

• Octal

Answer explanation

The base-2 number system is known as Binary, which uses only two digits: 0 and 1. In contrast, Decimal is base-10, Hexadecimal is base-16, and Octal is base-8. Therefore, the correct answer is Binary.

What is the binary representation of the decimal number 10?

• 1010

• 1001

• 1100

• 1000

Answer explanation

The binary representation of the decimal number 10 is 1010. This is derived from converting 10 into binary, where 1s and 0s represent powers of 2. Thus, the correct answer is 1010.

How many bits are in a byte?

• 4

• 8

• 16

• 32

Answer explanation

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

Which hexadecimal digit corresponds to the binary number 1111?

• E

• A

• F

• D

Answer explanation

The binary number 1111 corresponds to the decimal number 15. In hexadecimal, 15 is represented as F. Therefore, the correct answer is F.

What is the primary reason for using hexadecimal numbers in computing?

• Hexadecimal numbers are easier to understand for humans

• Computers can process hexadecimal numbers faster

• Hexadecimal numbers use less memory

• Hexadecimal numbers are more secure

Answer explanation

Hexadecimal numbers are more compact than binary, allowing for easier representation of data. This means they can represent larger values using fewer digits, effectively using less memory compared to other numeral systems.

The number system that uses only the digits 0 and 1 is called _______.

• binary

• decimal

• octal

• hexadecimal

Answer explanation

The number system that uses only the digits 0 and 1 is called binary. Unlike decimal (base 10), octal (base 8), and hexadecimal (base 16), binary is specifically designed for digital systems, making it the correct choice.

The number system that includes the digits 0 to 9 and the letters A to F is known as _______.

• hexadecimal

• binary

• octal

• decimal

Answer explanation

The hexadecimal number system uses digits 0-9 and letters A-F to represent values. It is base 16, making it distinct from binary (base 2), octal (base 8), and decimal (base 10). Thus, the correct answer is hexadecimal.

What is the decimal equivalent of the binary number 1011?

• 9

• 10

• 11

• 12

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 decimal equivalent is 11.

Which of the following is a base-16 number system?

• Binary

• Decimal

• Octal

• Hexadecimal

Answer explanation

The base-16 number system is known as hexadecimal. It uses digits 0-9 and letters A-F to represent values. In contrast, binary is base-2, decimal is base-10, and octal is base-8.

How many hexadecimal digits are needed to represent a byte?

• 1

• 2

• 4

• 8

Answer explanation

A byte consists of 8 bits. Each hexadecimal digit represents 4 bits. Therefore, to represent a byte, you need 2 hexadecimal digits (4 bits each), making the correct answer 2.