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Data, Information and Data Representation

Converting decimal to binary

  • 3 things to know
  • AS Unit 2

Overview

Decimal, denary and base 10 as the same system, the place values of an eight-bit number, and worked conversions from decimal into binary by repeated subtraction of place values.

What you need to know

Answer each one before you reveal it.

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Key term

What do the terms decimal, denary and base 10 all refer to?

Key term

Which eight place values make up an 8-bit binary number?

Key term

What is 45 as an 8-bit binary number?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What do the terms decimal, denary and base 10 all refer to?

    Model answer

    Decimal, denary and base 10 are three names for the ordinary counting system, which uses the ten digits 0 to 9 and gives each column a place value ten times the one to its right. Examination papers use decimal and denary interchangeably.

  2. 2

    Describe the place value method of converting a denary number to 8-bit binary.

    Model answer

    The place values 128, 64, 32, 16, 8, 4, 2 and 1 are written out, and working from the left each one is given a 1 if it can be taken from what is left of the number and a 0 if it cannot.

  3. 3

    Describe the repeated division method of converting denary to binary.

    Model answer

    The number is divided by 2 over and over, the remainder from each division is written down, and reading the remainders from the last one back to the first gives the binary number.

  4. 4

    Which eight place values make up an 8-bit binary number?

    Model answer

    The eight place values are 128, 64, 32, 16, 8, 4, 2 and 1.

  5. 5

    What is 45 as an 8-bit binary number?

    Model answer

    The value 45 is 00101101, because 32 plus 8 plus 4 plus 1 comes to 45.

  6. 6

    Convert 200 to 8-bit binary.

    Model answer

    The value 200 is 11001000, because 128 plus 64 plus 8 comes to 200.

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