1.4.1a Primitive Data Types & Binary — OCR H446

Primitive Data Types

A primitive data type is a basic data type built into the programming language. They are not composed of other types. The main primitive types in OCR H446 are:

Type	Example values	Stored as	Typical size
Integer	-3, 0, 42, 10000	Two's complement binary	32 or 64 bits
Real / Float	3.14, -0.001, 2.0	Floating point (IEEE 754)	32 or 64 bits
Boolean	True, False	0 (False) or 1 (True)	1 bit (often 1 byte)
Character	'A', '?', '5'	ASCII or Unicode code point	8 bits (ASCII), 8–32 bits (Unicode)
String	"Hello", "123"	Sequence of character code points	Variable (n × char size)

Note: a string is not truly primitive (it's a sequence of characters) but is often treated as a built-in type. OCR H446 includes it as a data type you must know.

Unsigned Binary Representation

All data in a computer is stored as binary (base 2) — sequences of 0s and 1s. An unsigned integer represents only non-negative values.

Each bit position has a place value that doubles as you move left:

Bit position	7	6	5	4	3	2	1	0
Place value	128	64	32	16	8	4	2	1

Converting Denary to Binary

Method: repeatedly divide by 2 and record remainders (bottom-up).

Example: Convert 75 to 8-bit binary 75 ÷ 2 = 37 r 1
37 ÷ 2 = 18 r 1
18 ÷ 2 = 9 r 0
9 ÷ 2 = 4 r 1
4 ÷ 2 = 2 r 0
2 ÷ 2 = 1 r 0
1 ÷ 2 = 0 r 1
Reading remainders bottom-up: 0100 1011
Check: 64+8+2+1 = 75 ✓

Converting Binary to Denary

Multiply each bit by its place value and sum the results.

Example: Convert 1011 0110 to denary 128×1 + 64×0 + 32×1 + 16×1 + 8×0 + 4×1 + 2×1 + 1×0
= 128 + 32 + 16 + 4 + 2 = 182

Hexadecimal

Hexadecimal (base 16) is a compact way to represent binary. Each hex digit represents exactly 4 bits (one nibble).

Denary	Binary	Hex	Denary	Binary	Hex
0	0000	0	8	1000	8
1	0001	1	9	1001	9
2	0010	2	10	1010	A
3	0011	3	11	1011	B
4	0100	4	12	1100	C
5	0101	5	13	1101	D
6	0110	6	14	1110	E
7	0111	7	15	1111	F

Binary → Hex: Group into nibbles from the right 1011 0110 → B 6 → B6 (hex)

Hex → Binary: Replace each digit with 4-bit binary 3F → 0011 1111 → 0011 1111

Hex → Denary: Use place values (16¹, 16⁰) B6 → (11×16) + (6×1) = 176 + 6 = 182

Data Storage Units

Unit	Size
Bit	1 binary digit (0 or 1)
Nibble	4 bits
Byte	8 bits
Kilobyte (KB)	1,000 bytes (SI) or 1,024 bytes (KiB)
Megabyte (MB)	1,000,000 bytes (SI) or 1,048,576 bytes (MiB)
Gigabyte (GB)	10⁹ bytes (SI) or 2³⁰ bytes (GiB)
Terabyte (TB)	10¹² bytes (SI)

Number Ranges

With n bits, the number of distinct values that can be represented = 2ⁿ.

Unsigned n-bit integer: range 0 to 2ⁿ − 1
8-bit unsigned: 0 to 255 (2⁸−1)
16-bit unsigned: 0 to 65535 (2¹⁶−1)

Why Binary? Why Hexadecimal?

Computers use binary because digital circuits have two stable states (high/low voltage = 1/0). Hexadecimal is used as a shorthand because:

Long binary strings are hard to read and error-prone
Each hex digit maps exactly to 4 bits — easy conversion
Used in: memory addresses, colour codes (#FF5733), MAC addresses, IP addresses in IPv6, machine code debugging

Exam tip: To convert denary to binary, use the subtraction method: write out place values (128, 64, 32, 16, 8, 4, 2, 1), then subtract each from the number (put 1 if it fits, 0 if not). Practice both directions until you can do them without thinking.

Exam tip: Know hex digits A=10, B=11, C=12, D=13, E=14, F=15. To convert B6 to denary: B=11, so B6 = 11×16 + 6 = 182. To convert binary to hex: split into 4-bit groups from the right.

⚠ Common Mistakes

Forgetting to pad binary to 8 bits — 75 in binary is 01001011, not just 1001011. Always give the requested number of bits.
Thinking hex only goes 0–9 — remember A through F represent 10–15. The digit F = 15 = 1111 in binary.
Confusing a string representation of a number with its numeric value — '123' is a string (characters '1','2','3'), not the integer 123. A character is not the same as its ASCII code.

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Worksheet — 1.4.1a Primitive Data Types & Binary

8 questions · 20 marks · instantly marked

Q1Name five primitive data types and for each give one example value and describe how it is stored in binary.[5 marks]

✓ Mark scheme

Integer (e.g. 42) — stored as two's complement binary; Real/Float (e.g. 3.14) — stored as floating point (IEEE 754 with sign, exponent, mantissa); Boolean (e.g. True) — stored as 0 (False) or 1 (True); Character (e.g. 'A') — stored as ASCII or Unicode code point (e.g. 'A' = 65 = 01000001); String (e.g. "Hello") — stored as a sequence of character code points. 1 mark for each type with correct example and storage description, up to 5.

Q2Convert the denary number 137 to 8-bit unsigned binary. Show your working.[3 marks]

✓ Mark scheme

Place values: 128 64 32 16 8 4 2 1. 137 ≥ 128 → 1, remainder 9. 9 < 64 → 0. 9 < 32 → 0. 9 < 16 → 0. 9 ≥ 8 → 1, remainder 1. 1 < 4 → 0. 1 < 2 → 0. 1 ≥ 1 → 1. Answer: 1000 1001 [3 marks — 1 for correct method, 1 for leading 1 at position 7, 1 for correct final answer]. Check: 128+8+1 = 137 ✓

Q3Convert the 8-bit binary number 01110101 to denary.[2 marks]

✓ Mark scheme

0×128 + 1×64 + 1×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1 [1 for correct working/method] = 64+32+16+4+1 = 117 [1 for correct answer].

Q4Convert the hexadecimal number A9 to (a) binary and (b) denary.[3 marks]

✓ Mark scheme

(a) A = 1010, 9 = 1001 → binary: 1010 1001 [1]; (b) A9 in denary: A=10, so 10×16 + 9×1 = 160+9 = 169 [2 — 1 for correct working, 1 for correct answer].

Q5Convert the 8-bit binary number 11001110 to hexadecimal.[2 marks]

✓ Mark scheme

Split into nibbles: 1100 | 1110. 1100 = 12 = C; 1110 = 14 = E [1 for correct split and identification]; Answer: CE [1 for correct final answer].

Q6How many distinct values can be represented using 10 bits? What is the maximum unsigned integer that can be stored?[2 marks]

✓ Mark scheme

Number of distinct values = 2¹⁰ = 1024 [1]; Maximum unsigned value = 2¹⁰ − 1 = 1023 [1] (since values range from 0 to 1023).

Q7Give two reasons why hexadecimal is used in computing rather than binary for representing data.[2 marks]

✓ Mark scheme

Any two from: Hexadecimal is more compact/shorter to write — fewer digits needed to represent the same value [1]; Each hex digit maps exactly to 4 bits, making conversion between hex and binary fast and easy without calculation [1]; Long binary strings are difficult to read and easy to make errors in — hex is more human-readable [1]; Hexadecimal is widely used in debugging, memory addresses, colour codes, MAC addresses [1].

Q8Explain the difference between an integer and a real (float) data type. Give one example of a situation where each would be the appropriate choice.[3 marks]

✓ Mark scheme

Integer: whole number (positive, negative or zero); stored as two's complement binary; no fractional part [1]. Real/Float: number with a fractional part; stored as floating point (sign, exponent, mantissa/significand); can represent very large or very small values [1]. Example — integer: counting items in a shopping basket, loop counter, age in years; real: measuring temperature (36.6°C), price (£4.99), GPS coordinates [1].

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Term	Definition

Primitive Data Types

Unsigned Binary Representation

Converting Denary to Binary

Converting Binary to Denary

Hexadecimal

Data Storage Units

Number Ranges

Why Binary? Why Hexadecimal?

Worksheet — 1.4.1a Primitive Data Types & Binary

Mini Test — 1.4.1a Data Types & Binary