2.6 Binary shifts

Question 1

When are binary shifts used?

Answer 1

when multiplying or dividing binary numbers by powers of 2

Question 2

multiplying binary numbers by powers of 2

Answer 2

x 2[2] shift 2 places etc.

multiplies the answer by 2 like denary multiplies by 10

a 0 is placed on the right

Question 3

dividing binary numbers by powers of 2

Answer 3

when you divide by powers of 2 you move bits to the right - right shifts

a 0 is placed at the leftmost place

Question 4

Multiply 00011110 by 2[2] [1]

Answer 4

01111000

Question 5

a) Explain how a binary number can be multiplied by 8 by shifting bits [3]

b) Complete a 3-place right shift on the binary number 10110100.
Explain why there is a loss in precision. [2]

Answer 5

a) 8 is equal to 2[3] so all the bits should be moved 3 places to the left
0s should be inserted into the three rightmost positions

b) 00010110

10110100 in denary/8 is 22.5

00010110 in denary is 22, which is less than 22.5

this is because the answer is given as the nearest lower integer in a right binary shift as the number doesn’t have decimals, so some precisions is lost