1.2.15

Number Bases

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Binary

In everyday life, we use the denary number system. Computers use binary instead.

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Denary

  • In everyday life, we use a denary number system.
  • We use 10 symbols to represent each digit.
  • Each digit's place value is multiplied by 10 as we move from right to left.
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Binary

  • Binary is an identical system, except using two symbols for each digit.
  • Only 1 and 0 are used in binary.
  • Each digit's place value is multiplied by two as we move from right to left.
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Hexadecimal

  • Hexadecimal uses 16 different symbols for each place.
  • Hexadecimal uses the digits 0-9 then A-F:
    • A = 10 in denary, B = 11 ...
  • Each digit's place value is multiplied by 16 as we move from right to left.

Converting Binary and Hexadecimal

Both binary and hexadecimal can be used to represent the same number, so it's important to be able to convert between them.

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Binary to hexadecimal

  • Binary can be converted to hexadecimal by grouping into groups of 4 bits:
    • Start grouping from the right-hand side.
    • Convert each 4 bit group separately.
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Hexadecimal to binary

  • Hexadecimal can be converted to binary by splitting each digit into 4 bits:
    • Separately convert each hexadecimal digit into 4 bits of binary.
    • Put all of the 4 bit groups together.

Converting Denary and Hexadecimal

Both denary and hexadecimal can be used to represent the same number, so it's important to be able to convert between them.

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Denary to hexadecimal

  • The easiest method to convert denary numbers to hexadecimal is to first convert the denary to binary, and then use the binary to hexadecimal conversion algorithm.
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Hexadecimal to denary

  • To convert from hexadecimal to denary, you should:
    • Write out the powers of 16 above each hexadecimal digit.
    • For each place column, multiply the hexadecimal digit by the power of 16 above it.
    • Add together all of these results.

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1Computer Systems

1.1Systems Architecture

1.2Memory & Storage

1.3Computer Networks, Connections & Protocols

1.4Network Security

1.5Systems Software

1.6Ethical, Legal, Cultural & Environmental Concern

2Computational Thinking, Algorithms and Programming

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