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AQA A-Level Computer Science
5.0 Fundamentals of data representation
5.3 Data representation
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What are the digits used in the binary number system?
0 and 1
The base of the binary number system is
2
The binary number system is directly suitable for computers because it aligns with
voltage levels
.
Match the advantage of using binary in computers with its description:
Simple implementation ↔️ Uses only two states: on/off
High reliability ↔️ Low number of states reduces errors
Efficient data storage ↔️ Requires minimal memory space
How many digits does the hexadecimal number system use?
16
The digits in the hexadecimal system include 0-9 and
A-F
Each hexadecimal digit corresponds to four
binary digits
.
Steps to convert a binary number to decimal:
1️⃣ Identify each digit's place value (powers of 2 from right to left)
2️⃣ Multiply each digit by its place value
3️⃣ Sum the products
To convert a decimal number to binary, you divide by
2
What is the value of the hexadecimal digit A in decimal?
10
When converting binary to hexadecimal, you group the binary digits into
sets
of four.
Match the conversion type with its method:
Binary to Decimal ↔️ Multiply by powers of 2
Decimal to Binary ↔️ Divide by 2 repeatedly
Hexadecimal to Decimal ↔️ Multiply by powers of 16
Decimal to Hexadecimal ↔️ Divide by 16 repeatedly
Binary to Hexadecimal ↔️ Group into sets of four
Hexadecimal to Binary ↔️ Convert each digit to four bits
Why is hexadecimal useful for representing binary data?
Uses fewer digits
Hexadecimal numbers are easy to convert to
binary
numbers.
The hexadecimal number system is a base-
16
Match the number system with its base:
Hexadecimal ↔️ 16
Decimal ↔️ 10
Binary ↔️ 2
The digits in the hexadecimal number system are 0-9 and
A-F
The decimal number system is the natural language of digital circuits.
False
What is the method for converting a binary number to decimal?
Multiply by powers of 2
To convert a decimal number to binary, you divide by
2
Steps to convert a decimal number to binary:
1️⃣ Divide the decimal number by 2
2️⃣ Record the remainder (0 or 1)
3️⃣ Repeat the division until the quotient is 0
4️⃣ Write the remainders in reverse order
What is the method for converting a hexadecimal number to decimal?
Multiply by powers of 16
To convert a decimal number to hexadecimal, you divide by
16
How do you convert a binary number to hexadecimal?
Group in sets of four
Converting a hexadecimal digit to binary involves writing four
bits
for each digit.
Match the number system with its conversion method:
Binary to Decimal ↔️ Multiply by powers of 2
Decimal to Hexadecimal ↔️ Divide by 16 and record remainders
Hexadecimal to Binary ↔️ Convert each digit to four bits
Decimal to Binary ↔️ Divide by 2 and record remainders
Unsigned integers can only represent non-
negative
values.
Unsigned integers use one bit to indicate the sign of the number.
False
What are the two main components of floating-point representation?
Mantissa and exponent
Floating-point numbers are suitable for scientific and engineering
calculations
.
Floating-point numbers have unlimited precision.
False
Floating-point numbers are often represented in normalized form to ensure maximum
precision
Floating-point numbers can represent
fractions
and decimals, unlike integers.
Floating-point numbers have limited precision due to a fixed number of bits for the mantissa and
exponent
What is an example of a floating-point number in normalized form?
1.234
×
1
0
5
1.234 \times 10^{5}
1.234
×
1
0
5
Character encoding standards define how text characters are represented as
binary values
in computers.
ASCII supports only 128 characters and has a range from
0
to 127.
How many characters does Unicode support?
Over 143,000
Order the following encoding standards based on compatibility with ASCII:
1️⃣ UTF-8
2️⃣ ASCII
What is an advantage of using Unicode in multilingual documents?
Supports vast range of characters
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