## Podcast Beta

## Questions and Answers

What is the denary number for the hexadecimal number C616?

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

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

What is the hexadecimal number for the binary number 001010112?

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

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What type of manipulation do shifts represent in bit patterns?

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

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What is the value of A in hexadecimal?

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What is the purpose of the hexadecimal system?

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What is the base of the hexadecimal counting system?

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

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

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

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

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What is the result of deducting 6410 from 7010?

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

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

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

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## 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.