Binary arithmetic

Quick links

3.3.1

Number bases

3.3.2

Converting 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

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

3.2 Programming

3.3 Fundamentals of data representation

3.4 Computer systems

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

3.8 Aspects of software development

Glossary and other links

Glossary of computing terms.

AQA 8520: The 2016 syllabus