Binary arithmetic

Lesson

Binary addition

Binary Shift

The binary shift operator is used to perform multiplication and division of numbers by powers of 2

multiply	x 16	x 8	x 4	x 2
shift	Left 4	Left 3	Left 2	Left 1

divide	/ 2	/ 4	/ 8
shift	Right 1	Right 2	Right 3

Example: Apply shift operator to 1101₂ (13₁₀)

Shift	Result	denary
Left 1	110102	1310 x 210 =2610
Left 2	1101002	1310 x 410 =5210
Right 1	1102	1310 /210 =610

Note that odd numbers are rounded down to the nearest integer when the right shift operator is applied.

Learning Videos

For more information click on the tab below to watch a video about the lesson.

Click for video - Adding three 8-bit binary integers

Click for video - Binary shifts

Questions

1. Apply a right shift of one binary place on the following byte.

   1

   0

   0

   1

   1

   1

   1

   0

   Convert the original and shifted binary numbers into decimal What is the effect of the logical binary shift?

   
   

   0

   1

   0

   0

   1

   1

   1

   1

   158 and 79

   Division by two.

2. Apply a right shift of one binary place on the following byte.

   0

   1

   0

   1

   1

   0

   1

   0

   Convert the original and shifted binary numbers into decimal What is the effect of the logical binary shift?

   
   

   1

   0

   1

   1

   0

   1

   0

   0

   90 and 180

   Multiply by two.

3. Add 00100111 to 00101010. You should include your working.

   
   

   0 1 0 1 0 0 0 1

4. Add 00100111 to 00111010. You should include your working.

   
   

   0 1 1 0 0 0 0 1

5. Show the result of adding the following three binary numbers. 110011 10111 101

   
   

   1 0 0 1 1 1 1