1.8 & 1.9 - Number Systems & Conversion

Exam Board:

OCR

Specification:

2016 - Unit 1 

What is binary?

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.

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.

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, 100111101011 is 9EB.

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

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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.

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Questo's Questions

1.8 & 1.9 - Number Systems:

1. Explain why hexadecimal numbers are used as an alternative to binary[2]

2. Convert the following values from binary to denary:

     a. 00101010

     b. 11011011

     c. 01011101

     d. 11101110

     e. 01011111  [1 each]

3. Convert the following values from denary to binary:

     a. 35

     b. 79

     c. 101

     d. 203

     e. 250  [1 each]

4. Convert the following values from binary to hexadecimal:

     a. 11110101

     b. 01100111

     c. 10111010

     d. 10010000

     e. 11101001  [1 each]

5. Convert the following values from hexadecimal to binary:

     a. C2

     b. 8A

     c. DE

     d. 54

     e. F7     [1 each]

6. Convert the following values from denary to hexadecimal:

     a. 134

     b. 201

     c. 57

     d. 224

     e. 101   [1 each]

7. Convert the following values from hexadecimal to denary:

     a. 32

     b. A5

     c. 88

     d. C0

     e. BE   [1 each]

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

Section 1.7 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.