Binary arithmetic
Quick links |
Number bases |
Converting number bases |
Units of information |
Binary arithmetic |
Character encoding |
Representing images |
Representing sound |
Data compression |
Syllabus content
Content | Additional Information | |
---|---|---|
Be able to add together up to three binary numbers. | Students will be expected to use a maximum of 8 bits and a maximum of 3 values to add. Answers will be a maximum of 8 bits in length and will not involve carrying beyond the eight bits. | |
Be able to apply a binary shift to a binary number. | Students will be expected to use a maximum of 8 bits. Students will be expected to understand and use only a logical binary shift. Students will not need to understand or use fractional representations. | |
Describe situations where binary shifts can be used. | Binary shifts can be used to perform simple multiplication/division by powers of 2 |
Starter
Convert 125 and 231 to binary
Convert 7DA to decimal
Convert 1011 0101 0011 to Hex
Exercise
Here is an example:
If in decimal number you add two numbers (say 6 + 7) how wold you have written that calculation in primary school?
6 add 7 gives 3 carry 1
In binary, the largest digit is 1 but the principle is the same.
1 add 1 (in binary) is 0 carry 1
Question 1
64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
---|---|---|---|---|---|---|---|---|
0 | 1 | 1 | 0 | 0 | 1 | 1 | ||
Question 2
64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 0 | 1 | 1 | 1 | 0 | 1 | ||
---|---|---|---|---|---|---|---|---|
0 | 1 | 1 | 1 | 0 | 1 | 0 | ||
Question 3
64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
1 | 0 | 1 | 1 | 1 | 0 | 1 | ||
---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 1 | 0 | 1 | 1 | ||
Question 4
64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
---|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 1 | 0 | 1 | ||
Question 5
64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 1 | 1 | 0 | 0 | 1 | 1 | ||
---|---|---|---|---|---|---|---|---|
0 | 1 | 1 | 0 | 0 | 1 | 1 | ||
Question 6
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | ||
---|---|---|---|---|---|---|---|---|---|
0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | ||
Question 7
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | ||
---|---|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | ||
Extension Question 1 (Use shift and add) to multiply 1101 by 101
16 | 8 | 4 | 2 | 1 | Decimal value | |
0 | 1 | 1 | 0 | 1 | ||
1 | 0 | 1 | ||||
Extension Question 2 (Use shift and add) to multiply 11101 by 1110
16 | 8 | 4 | 2 | 1 | Decimal value | |
1 | 1 | 1 | 0 | 1 | ||
1 | 1 | 1 | 0 | |||
Extension Question 3 (Use shift and add) to multiply 101101 by 1101
32 | 16 | 8 | 4 | 2 | 1 | Decimal value | |
1 | 0 | 1 | 1 | 0 | 1 | ||
1 | 1 | 0 | 1 | ||||
3.1 Fundamentals of algorithms
- 3.1.1 Representing algorithms
- 3.1.2 Efficiency of algorithms
- 3.1.3 Searching algorithms
- 3.1.4 Sorting algorithms

3.2 Programming
- 3.2.1 Data types
- 3.2.2 Programming concepts
- 3.2.3 Arithmetic operations in a programming language
- 3.2.4 Relational operations in a programming language
- 3.2.5 Boolean operations in a programming language
- 3.2.6 Data structures
- 3.2.7 Input/output and file handling
- 3.2.8 String handling operations in a programming language
- 3.2.9 Random number generation in a programming language
- 3.2.10 Subroutines (procedures and functions)
- 3.2.11 Structured programming
- 3.2.12 Robust and secure programming
- 3.2.13 Classification of programming languages

3.3 Fundamentals of data representation
- 3.3.1 Number bases
- 3.3.2 Converting between number bases
- 3.3.3 Units of information
- 3.3.4 Binary arithmetic
- 3.3.5 Character encoding
- 3.3.6 Representing images
- 3.3.7 Representing sound
- 3.3.8 Data compression

3.4 Computer systems
- 3.4.1 Hardware and software
- 3.4.1 Operating systems
- 3.4.2 Boolean logic
- 3.4.3 Software classification
- 3.4.4 Systems architecture

3.5 Fundamentals of computer networks

3.6 Fundamentals of cyber security

3.7 Ethical, legal and environmental impacts of digital technology on wider society, including issues of privacy
- 3.7.1 Ethical impacts of digital technology on wider society
- 3.7.2 Legal impacts of digital technology on wider society
- 3.7.3 Environmental impacts of digital technology on wider society
- 3.7.4 Issues of privacy

3.8 Aspects of software development

Glossary and other links
