Understanding Number Systems in IT

What is the binary equivalent of the decimal number 10?

• 1000

• 1010

• 1100

• 1110

Answer explanation

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

Which of the following is a characteristic of the binary number system?

• It uses digits 0 to 9.

• It is base 8.

• It uses digits 0 and 1.

• It is base 16.

Answer explanation

The binary number system is characterized by using only two digits: 0 and 1. This distinguishes it from other systems like decimal (0-9), octal (base 8), and hexadecimal (base 16). Thus, the correct choice is 'It uses digits 0 and 1.'.

Convert the decimal number 25 to binary.

• 11001

• 10101

• 11100

• 10011

Answer explanation

To convert 25 to binary, divide by 2 and record the remainders. 25 ÷ 2 = 12 R1, 12 ÷ 2 = 6 R0, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Reading the remainders from bottom to top gives 11001, which is the correct binary representation.

What is the hexadecimal equivalent of the binary number 1011?

• 9

• A

• B

• C

Answer explanation

The binary number 1011 converts to decimal 11. In hexadecimal, 11 is represented as B. Therefore, the correct answer is B.

How many bits are there 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.

Convert the decimal number 255 to hexadecimal.

• FF

• 1F

• F0

• 0F

Answer explanation

To convert 255 to hexadecimal, divide by 16. 255 ÷ 16 = 15 remainder 15. The quotient (15) is F and the remainder (15) is also F. Thus, 255 in hexadecimal is FF.

What is the decimal equivalent of the binary number 1111?

• 14

• 15

• 16

• 17

Answer explanation

To convert the binary number 1111 to decimal, calculate: 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 8 + 4 + 2 + 1 = 15. Thus, the decimal equivalent of 1111 is 15.

Which of the following is the binary representation of the hexadecimal number A?

• 1010

• 1100

• 1110

• 1001

Answer explanation

The hexadecimal number A is equivalent to 10 in decimal. The binary representation of 10 is 1010. Therefore, the correct answer is 1010.

Convert the binary number 1101 to decimal.

• 11

• 12

• 13

• 14

Answer explanation

To convert the binary number 1101 to decimal, calculate: 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13. Therefore, the correct answer is 13.

What is the base of the hexadecimal number system?

• 2

• 8

• 10

• 16

Answer explanation

The hexadecimal number system is a base-16 system, which means it uses 16 distinct symbols (0-9 and A-F) to represent values. Therefore, the correct answer is 16.