Number System Conversion Quiz: Binary, Octal, Hexadecimal

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Questions and Answers

What is the denary number for the hexadecimal number C616?

19810 (correct)

19210

6110

9616

What is the result of converting the hexadecimal number 2B16 to a binary number?

001010112 (correct)

110101112

101010112

011010112

What is the purpose of the Base 16 table in converting a hexadecimal number to a denary number?

To subtract each heading to obtain the denary converted number

To multiply each heading to obtain the denary converted number (correct)

To add each heading to obtain the denary converted number

To divide each heading to obtain the denary converted number

What is the hexadecimal number for the binary number 001010112?

2B16 Signup and view all the answers

What is the result of converting the denary number 19810 to a hexadecimal number?

C616 Signup and view all the answers

What type of manipulation do shifts represent in bit patterns?

Arithmetic shift functions Signup and view all the answers

What is the representation of the binary number 100010102 in the denary number system?

13810 Signup and view all the answers

What is the value of A in hexadecimal?

1010 Signup and view all the answers

What is the purpose of the hexadecimal system?

To make binary numbers more readable by humans Signup and view all the answers

What is the base of the hexadecimal counting system?

Base 16 Signup and view all the answers

What is the representation of the hexadecimal number 8A16 in the denary number system?

13810 Signup and view all the answers

In a binary number, what does the digit 0 represent?

The switch is OFF Signup and view all the answers

Why is it easier to say 8A16 instead of 100010102 in a telephone conversation?

Because 8A16 is less prone to mistakes Signup and view all the answers

What is the base of the table used for converting denary to binary?

Base 2 Signup and view all the answers

What is the result of deducting 6410 from 7010?

610 Signup and view all the answers

What is the purpose of creating a Base 2 table when converting denary to binary?

To find the binary representation of a denary number Signup and view all the answers

What is the process for converting a denary number to binary?

Repeating the process of deducting the largest possible value from the remaining denary number Signup and view all the answers

What is the denary number being converted to binary in the example?

19810 Signup and view all the answers

Study Notes

Converting Between Number Systems

Converting between denary, binary, and hexadecimal number systems is important for clear communication.
Using hexadecimal numbers (e.g., 8A16) is easier and less prone to mistakes than reading out binary numbers (e.g., 100010102).

Denary to Binary

One way to convert a denary number to binary is by using a Base 2 table.
Start with the denary number and see if it is more than the first number on the left of the table.
If it is, write a 1 under the heading; if not, write a 0.
Repeat the process, deducting the previous number from the remaining number.

Binary to Hexadecimal

To convert a binary number to hexadecimal, use a shortcut by drawing two 4-bit Base 2 tables.
Represent the first number in the left-hand table and the second number in the right-hand table.
Join the two tables together to make a single 8-bit table.

Hexadecimal to Denary

To convert a hexadecimal number to denary, draw a Base 16 table.
Multiply each heading by the corresponding hexadecimal digit to obtain the denary number.

Hexadecimal System

The hexadecimal system is a Base 16 counting system.
It uses digits 0-9 and characters A-F to represent 10-15.
Hexadecimal numbers can be quickly converted from binary numbers.

Arithmetic Shift Functions

Shifts are manipulations of bit patterns.
A binary number is a string of bits, each representing a switch that is either ON (1) or OFF (0).

Interesting Facts

The hexadecimal system was used in traditional Chinese weights and measurements until the late 20th century.
Other cultures used different base counting systems, such as the ancient Babylonians' Base 60 system.

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Description

Learn how to convert between different number systems, including denary, binary, and hexadecimal. Understand how to read and write numbers in each system and avoid mistakes. Practice converting between these systems with this quiz.