Number Systems and Conversion Techniques

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What are the symbols used in the hexadecimal number system?

The symbols used in the hexadecimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

Which number systems are used by computers and which are used by humans?

Binary and hexadecimal number systems are used by computers, while the decimal system is used by humans.

Convert the decimal number 10 to its binary equivalent.

The binary equivalent of the decimal number 10 is 1010.

What is the base of the octal number system, and what symbols does it use?

The base of the octal number system is 8, and it uses the symbols 0, 1, 2, 3, 4, 5, 6, and 7. Signup and view all the answers

What is the result of converting the binary number 1111 to decimal?

The binary number 1111 converts to the decimal number 15. Signup and view all the answers

How would you express the decimal number 25 in hexadecimal?

The decimal number 25 can be expressed in hexadecimal as 19. Signup and view all the answers

Describe the main difference between binary and decimal number systems.

The binary number system is base 2 and uses two symbols (0 and 1), while the decimal system is base 10 and uses ten symbols (0-9). Signup and view all the answers

What is the binary representation of the decimal number 117?

The binary representation of 117 is <code>1110101</code>. Signup and view all the answers

How is the value of 'k' defined in base 2 powers?

'k' in base 2 powers represents 2¹⁰, which equals 1024. Signup and view all the answers

Illustrate the addition of binary numbers 10101 and 11001.

The addition results in <code>101110</code>. Signup and view all the answers

What is the hexadecimal value of the decimal number 451?

The hexadecimal value of 451 is <code>1C3</code>. Signup and view all the answers

Using the rule for multiplying powers, what is the result of 2⁶ * 2¹⁰?

The result is <code>2¹⁶</code>, which equals 65,536. Signup and view all the answers

What is the octal equivalent of the binary number $1011010111_2$?

1327_8 Signup and view all the answers

How do you convert the binary number $1010111011_2$ to hexadecimal?

2BB_{16} Signup and view all the answers

Explain the technique used to convert octal $1076_8$ to hexadecimal.

Use binary as an intermediary. Signup and view all the answers

What is the binary representation of the octal number $703_8$?

1110111 Signup and view all the answers

What binary number corresponds to the hexadecimal value $1AF$?

000110101111 Signup and view all the answers

What is the correct binary conversion process for the octal digit 6?

110 Signup and view all the answers

Convert the binary number $1110101_2$ to octal.

725_8 Signup and view all the answers

What is the octal equivalent of the hexadecimal number $1F0C_{16}$?

17414_8 Signup and view all the answers

How do you convert the binary number $101010_2$ to octal?

52_8 Signup and view all the answers

What is the hexadecimal equivalent of the binary number $11110000_2$?

F0_{16} Signup and view all the answers

What method is used to convert a decimal number to binary?

Divide the number by two and track the remainders. Signup and view all the answers

Convert the decimal number $125_{10}$ to binary.

$125_{10} = 1111101_2$ Signup and view all the answers

How do you convert the decimal fraction $0.6875_{10}$ to binary?

$0.6875_{10} = 0.1011_2$ Signup and view all the answers

Explain the technique for converting binary to decimal.

Multiply each bit by $2^n$, where n is the position index of the bit. Signup and view all the answers

Convert the binary number $101011_2$ to decimal.

$101011_2 = 43_{10}$ Signup and view all the answers

What is the conversion process from octal to decimal?

Multiply each digit by $8^n$, where n is the position index starting from 0 on the right. Signup and view all the answers

Convert the octal number $724_8$ to decimal.

$724_8 = 468_{10}$ Signup and view all the answers

Describe how to convert hexadecimal numbers to decimal.

Multiply each digit by $16^n$, where n is the bit's position starting from 0. Signup and view all the answers

What is the decimal equivalent of a hexadecimal number such as $1A3_{16}$?

This evaluates to $1 imes 16^2 + 10 imes 16^1 + 3 imes 16^0 = 419_{10}$ Signup and view all the answers

What is the decimal equivalent of the hexadecimal number $C3F_{16}$?

1631 Signup and view all the answers

Convert the octal number $257_8$ to binary.

010 101 111 Signup and view all the answers

What is the binary equivalent of the hexadecimal number $3B7_{16}$?

0011 1011 0111 Signup and view all the answers

How would you express $97_{10}$ in octal?

141_8 Signup and view all the answers

If the decimal number $0.625_{10}$ is converted to octal, what is the result?

0.5_8 Signup and view all the answers

Find the octal equivalent of $456.75_{10}$.

710.6_8 Signup and view all the answers

What is the hexadecimal representation of the decimal number $255_{10}$?

FF_{16} Signup and view all the answers

Convert the decimal number $(7.125)_{10}$ to octal.

7.1_8 Signup and view all the answers

What is the decimal result of $B2D_{16}$?

2861 Signup and view all the answers

Study Notes

Number Systems

Decimal system uses base 10, with symbols 0-9. Used by humans.
Binary system uses base 2, with symbols 0 and 1. Used by computers.
Octal system uses base 8, with symbols 0-7.
Hexadecimal system uses base 16, with symbols 0-9 and A-F. Used by computers.

Conversion Techniques

Decimal to Binary: Divide the decimal number by 2 repeatedly, keeping track of the remainders. The remainders in reverse order form the binary equivalent.
Decimal to Octal: Divide the decimal number by 8 repeatedly, keeping track of the remainders.
Decimal to Hexadecimal: Divide the decimal number by 16 repeatedly, keeping track of the remainders. Convert remainders greater than 9 to their hexadecimal equivalent (A=10, B=11, C=12, D=13, E=14, F=15).
Binary to Decimal: Multiply each bit by 2 raised to the power of its position (starting from 0 on the right). Sum the results.
Octal to Decimal: Multiply each octal digit by 8 raised to the power of its position (starting from 0 on the right). Sum the results.
Hexadecimal to Decimal: Multiply each hexadecimal digit by 16 raised to the power of its position (starting from 0 on the right). Sum the results.
Octal to Binary: Convert each octal digit to its 3-bit binary equivalent.
Hexadecimal to Binary: Convert each hexadecimal digit to its 4-bit binary equivalent.
Binary to Octal: Group the bits in threes (starting from the right). Convert each group to its octal equivalent.
Binary to Hexadecimal: Group the bits in fours (starting from the right). Convert each group to its hexadecimal equivalent.
Octal to Hexadecimal: Convert the octal number to binary, then convert the binary number to hexadecimal.

Common Powers of 2

2¹⁰ = 1024 (kilo)
2²⁰ = 1,048,576 (Mega)
2³⁰ = 1,073,741,824 (Giga)

Binary Arithmetic

Binary addition and multiplication follow rules similar to decimal arithmetic.

Additional Notes

Common number systems include decimal, binary, octal, and hexadecimal
Understanding conversion between different number systems is critical for many computer science applications.
Specific arithmetic rules apply for each number system.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers various number systems, including decimal, binary, octal, and hexadecimal, as well as the conversion techniques used between these systems. Test your understanding of how to convert numbers from one base to another using the methods described here.