Exam Board:
OCR
2.4a: Number Systems
Specification:
J277
Watch on YouTube:
Binary and Denary
Hexadecimal
Number System Ranges
Binary to Denary
Denary to Binary
What is binary?
By now you should know that computer systems process data and communicate entirely in binary.
​
Topic 2.3 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.
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.
Binary & Denary
Convert from binary to denary:
Convert from denary to binary:
Hexadecimal
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 in binary is 9EB in hexadecimal.
​
Hexadecimal only uses single-character values. Double-digit numbers are converted into letters - use the table on the right to help you understand.
Binary to hexadecimal:
Hexadecimal to binary:
Converting from denary to hexadecimal / hexadecimal to denary
To convert from denary to hexadecimal or from hexadecimal to denary, it is easiest to convert to binary first.​
​
However, it is possible to convert directly from denary to hexadecimal or directly from hexadecimal to denary. The videos below explain both methods.
Denary to hexadecimal:
Hexadecimal to denary:
Watch on YouTube
Watch on YouTube
Questo's Questions
2.4a - 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
-
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]
Click the banners below to try self-marking quizzes (Google Forms) on these topics.
Binary to Denary:
Denary to Binary:
Binary to Hexadecimal:
Hexadecimal to Binary: