78. OCR A Level (H046-H446) SLR13 - 1.4 Converting between binary, hex & denary

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Summary

This video explains how to convert positive integers between binary, hexadecimal, and denary number systems. It emphasizes using binary as an intermediary step for easier conversions and provides several examples for both directions of conversion.

Highlights

Introduction to Number System Conversion
00:00:00

The video introduces the topic of converting positive integers between binary, hexadecimal, and denary. A table is mentioned that facilitates these conversions, covering base 2, base 10, and base 16.

Converting Denary to Hexadecimal (Example 1: 12)
00:00:31

To convert denary number 12 to hexadecimal, the first step is to convert 12 into its binary representation (0000 1100). Then, the binary number is grouped into 'nibbles' (groups of four bits). The right nibble (1100) represents 12, which is 'C' in hexadecimal, and the left nibble (0000) represents 0, resulting in '0C' or simply 'C'.

Converting Denary to Hexadecimal (Example 2: 24)
00:01:58

For denary 24, it's first converted to binary (0001 1000). The right nibble (1000) is 8 in denary, so it's 8 in hex. The left nibble (0001) is 1 in denary, so it's 1 in hex. Thus, 24 in denary is '18' in hexadecimal, not '18' as a single number but 'one eight'.

Converting Denary to Hexadecimal (Example 3: 230)
00:03:32

The denary number 230 is converted to binary (1110 0110). The left nibble (1110) sums to 14, which is 'E' in hexadecimal. The right nibble (0110) sums to 6. Therefore, 230 in denary is 'E6' in hexadecimal.

Converting Denary to Hexadecimal (Example 4: 100)
00:04:50

The denary number 100 is converted to binary (0110 0100). The left nibble (0110) sums to 6. The right nibble (0100) sums to 4. So, 100 in denary is '64' in hexadecimal, pronounced 'six four'.

Converting Hexadecimal to Binary and Denary (Example 1: AB)
00:06:07

To convert hexadecimal 'AB' to denary, first convert each hex digit to its 4-bit binary nibble. 'A' (10) becomes 1010, and 'B' (11) becomes 1011. Concatenating these gives 10101011 in binary. Adding the denary values of the bits set to 1 (128 + 32 + 8 + 2 + 1) results in 171.

Converting Hexadecimal to Binary and Denary (Example 2: 36)
00:07:42

Hexadecimal '36' is converted by transforming '3' into 0011 and '6' into 0110. The combined binary is 00110110. Summing the positional values of the '1's (32 + 16 + 4 + 2) yields 54 in denary.

Converting Hexadecimal to Binary and Denary (Example 3: 7F)
00:08:43

For hexadecimal '7F', '7' converts to 0111 and 'F' (15) converts to 1111. The full binary is 01111111. Adding the denary values (64 + 32 + 16 + 8 + 4 + 2 + 1) gives 127 in denary.

Conclusion
00:09:49

The video concludes by reiterating the importance of understanding how to convert between binary, denary, and hexadecimal number systems.

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