IB Computer Science Topic A1.2.1 Principal Methods of Representing Data Revision Notes (SL/HL)

IB Computer Science Topic A1.2.1 Principal Methods of Representing Data Revision Notes (SL/HL) | RevisionDojo

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Data Representation

Definition

Data Representation

Computers store and process data as numbers, specifically in binary. Since modern computer architecture relies on transistors which are either On (1) or Off (0)

Analogy

A light switch has two states, on and off. Computers work the same way with 1s and 0s.

The Representation of Integers in Binary

Definition

Binary

Binary is a base-2 number system, using only two digits: 0 and 1. Each digit in a binary number is called a bit (short for binary digit).

Place Value in Binary

Each bit position represents a power of 2, starting from $2^0$ at the rightmost bit and increasing to the left.
Example: The binary number $1011_2$ can be broken down as follows:

Bit	0	0	0	0	1	0	1	1
Place Value	$$2^7$$	$$2^6$$	$$2^5$$	$$2^4$$	$$2^3$$	$$2^2$$	$$2^1$$	$$2^0$$
Place Value	128	64	32	16	8	4	2	1
Decimal Value	0	0	0	0	8	0	2	1

Calculation: $1 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1 = 11_{10}$

Note

Binary is the most compact representation for computers, as it directly aligns with their hardware, which uses transistors operating in two states.

Converting Binary to Decimal

Identify the Place Values: Each bit represents a power of 2.
Multiply Each Bit by Its Place Value: For each 1 in the binary number, multiply it by the corresponding power of 2.
Add the Products: Sum the results to get the decimal value.

Example question

Convert $1011_2$ to decimal.

Solution

Place Values: $2^3, 2^2, 2^1, 2^0$
Multiplication: $1 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1$
Sum: $8 + 0 + 2 + 1 = 11_{10}$

Tip

When converting binary to decimal, it can be helpful to read the binary number from right to left, aligning each bit with its corresponding power of 2.
Draw it out in a table if necessary

Place Value	128	64	32	16	8	4	2	1
Binary	1	0	1	1	0	0	1	1
Calculation	(128 x 1)	+ 0	+ (32 x 1)	+ (16 x 1)	+ 0	+ 0	+ (2 x 1)	+ (1 x 1)

Converting Decimal to Binary

Divide the Decimal Number by 2: Record the remainder (0 or 1).
Repeat: Continue dividing the quotient by 2 until it reaches 0.
Write the Remainders in Reverse Order: This forms the binary number.

Example question

Convert $13_{10}$ to binary.

Solution

$13 \div 2 = 6$ R1
$6 \div 2 = 3$ R0
$3 \div 2 = 1$ R1
$1 \div 2 = 0$ R1

Binary: $1101_2$

Method 2: Subtraction Method

Start from largest power of 2 that fits

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Data Representation

Definition

Data Representation

Computers store and process data as numbers, specifically in binary. Since modern computer architecture relies on transistors which are either On (1) or Off (0)

Analogy

A light switch has two states, on and off. Computers work the same way with 1s and 0s.

The Representation of Integers in Binary

Definition

Binary

Binary is a base-2 number system, using only two digits: 0 and 1. Each digit in a binary number is called a bit (short for binary digit).

Place Value in Binary

Each bit position represents a power of 2, starting from $2^0$ at the rightmost bit and increasing to the left.
Example: The binary number $1011_2$ can be broken down as follows:

Bit	0	0	0	0	1	0	1	1
Place Value	$$2^7$$	$$2^6$$	$$2^5$$	$$2^4$$	$$2^3$$	$$2^2$$	$$2^1$$	$$2^0$$
Place Value	128	64	32	16	8	4	2	1
Decimal Value	0	0	0	0	8	0	2	1

Calculation: $1 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1 = 11_{10}$

Note

Binary is the most compact representation for computers, as it directly aligns with their hardware, which uses transistors operating in two states.

Converting Binary to Decimal

Identify the Place Values: Each bit represents a power of 2.
Multiply Each Bit by Its Place Value: For each 1 in the binary number, multiply it by the corresponding power of 2.
Add the Products: Sum the results to get the decimal value.

Example question

Convert $1011_2$ to decimal.

Solution

Place Values: $2^3, 2^2, 2^1, 2^0$
Multiplication: $1 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1$
Sum: $8 + 0 + 2 + 1 = 11_{10}$

Tip

When converting binary to decimal, it can be helpful to read the binary number from right to left, aligning each bit with its corresponding power of 2.
Draw it out in a table if necessary

Place Value	128	64	32	16	8	4	2	1
Binary	1	0	1	1	0	0	1	1
Calculation	(128 x 1)	+ 0	+ (32 x 1)	+ (16 x 1)	+ 0	+ 0	+ (2 x 1)	+ (1 x 1)

Converting Decimal to Binary

Divide the Decimal Number by 2: Record the remainder (0 or 1).
Repeat: Continue dividing the quotient by 2 until it reaches 0.
Write the Remainders in Reverse Order: This forms the binary number.

Example question

Convert $13_{10}$ to binary.

Solution

$13 \div 2 = 6$ R1
$6 \div 2 = 3$ R0
$3 \div 2 = 1$ R1
$1 \div 2 = 0$ R1

Binary: $1101_2$

Method 2: Subtraction Method

Start from largest power of 2 that fits

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Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

A1 Computer fundamentals4 subtopics

A2 Networks4 subtopics

A3 Databases4 subtopics

A4 Machine learning4 subtopics

B1 Computational thinking1 subtopic

B2 Programming5 subtopics

B3 Object-oriented programming2 subtopics

B4 Abstract data types (HL only)1 subtopic

IB Computer Science Topic A1.2.1: Principal Methods of Representing Data Notes

A1 Computer fundamentals4 subtopics

A2 Networks4 subtopics

A3 Databases4 subtopics

A4 Machine learning4 subtopics

B1 Computational thinking1 subtopic

B2 Programming5 subtopics

B3 Object-oriented programming2 subtopics

B4 Abstract data types (HL only)1 subtopic

Data Representation

The Representation of Integers in Binary

Place Value in Binary

Converting Binary to Decimal

Converting Decimal to Binary

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Data Representation

The Representation of Integers in Binary

Place Value in Binary

Converting Binary to Decimal

Converting Decimal to Binary

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