## 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

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

 0 0 64 32 16 8 4 2 1 Decimal value 1 0 1 1 0 1 1 1 0 0 1 1

Question 2

 0 0 64 32 16 8 4 2 1 Decimal value 0 1 1 1 0 1 1 1 1 0 1 0

Question 3

 1 0 64 32 16 8 4 2 1 Decimal value 0 1 1 1 0 1 0 1 1 0 1 1

Question 4

 0 0 64 32 16 8 4 2 1 Decimal value 1 0 1 1 0 1 1 0 1 1 0 1

Question 5

 0 0 64 32 16 8 4 2 1 Decimal value 1 1 0 0 1 1 1 1 0 0 1 1

Question 6

 1 0 0 1 128 64 32 16 8 4 2 1 Decimal value 1 1 0 0 1 1 1 0 1 0 1 1

Question 7

 0 0 0 1 128 64 32 16 8 4 2 1 Decimal value 1 1 1 1 1 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