4.1: Number Systems

Exam Board:

Eduqas / WJEC

Specification:

2020 + 

What is binary?

By now you should know that computer systems process data and communicate entirely in binary.

Topic 1.4 explained different binary storage units such as bits (a single 0 or 1), nibbles (4 bits) and bytes (8 bits).

Binary is a base 2 number system. This means that it only has 2 possible values - 0 or 1.

Because binary is a base 2 number system, binary numbers should be written out with a 2 after them, like this: 10101002

What is denary?

Denary (also known as decimal) is the number system that you've been using since primary school.

Denary is a base 10 number system. This means that it has 10 possible values - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Because denary is a base 10 number system, denary numbers should be written out with a 10 after them, like this: 16510

How to convert from binary to denary:

How to convert from denary to binary:

What is hexadecimal?

Hexadecimal is a base 16 number system. This means that it has 16 possible values - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Because hexadecimal is a base 16 number system, hexadecimal numbers should be written out with a 16 after them, like this: 6E16

Hexadecimal is used as a shorthand for binary because it uses fewer characters to write the same value. This makes hexadecimal less prone to errors when reading or writing it, compared to binary. For example, 1001111010112 is 9EB16.

Hexadecimal only uses single-character values. Double-digit numbers are converted into letters - use the table on the right to help you understand.

How to convert from binary to hexadecimal:

How to convert from hexadecimal to binary:

Converting from denary to hexadecimal / hexadecimal to denary

To convert from denary to hexadecimal or the other way round you must convert to binary first.

Denary > Binary > Hexadecimal

Hexadecimal > Binary > Denary

Use the videos on this page if you need help converting to or from binary.

The most common number systems question in exams are from denary to hexadecimal or from hexadecimal to denary so make sure that you practice these conversions.

Questo's Questions

4.1 - Number Systems:

1. Explain why hexadecimal numbers are used as an alternative to binary. Use an example[3]

2. Convert the following values from binary to denary:

  • a. 00101010 2

  • b. 110110112

  • c. 010111012

  • d. 11101110 2

  • e. 010111112     [1 each]

3. Convert the following values from denary to binary:

  • a. 35 10

  • b. 79 10

  • c. 101 10

  • d. 203 10

  • e. 250 10     [1 each]

4. Convert the following values from binary to hexadecimal:

  • a. 111101012

  • b. 011001112

  • c. 10111010 2

  • d. 10010000 2

  • e. 111010012      [1 each]

5. Convert the following values from hexadecimal to binary:

  • a. C2 16

  • b. 8A 16

  • c. DE 16

  • d. 54 16

  • e. F7 16      [1 each]

6. Convert the following values from denary to hexadecimal:

  • a. 134 10

  • b. 201 10

  • c. 57 10

  • d. 224 10

  • e. 101 10     [1 each]

7. Convert the following values from hexadecimal to denary:

  • a. 32 16

  • b. A5 16

  • c. 88 16

  • d. C0 16

  • e. BE 16    [1 each]

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