1.3 Binary Shifts and Two’s Complement

Question 1

What is the result of multiplying the binary number 0101 0101 1101 1101 by two?

Answer 1

1010 1011 1011 1010

To multiply a binary number by two, move all bits to the left and put a zero at the right.

Question 2

How do you divide a binary number by 2?

Answer 2

Move the bits to the right and put a zero in the most significant bit

Dividing by 2 results in a loss of precision for non-integer results.

Question 3

What happens to the fractional component when dividing an 8-bit binary number?

Answer 3

It is lost

Example: 45 ÷ 2 = 22.5 is represented as 22 in binary.

Question 4

What is the effect of a logical left shift on a binary number?

Answer 4

Doubles the number

Example: 1000 (8) becomes 10000 (16) after a left shift.

Question 5

What is the effect of a binary right shift on a number?

Answer 5

Halves the number and rounds down

Example: 1000 (8) becomes 100 (4) after a right shift.

Question 6

What is the range of numbers that can be represented using 8-bit Two’s Complement?

Answer 6

-128 to 127

Question 7

How is -15 represented in Two’s Complement?

Answer 7

1111 0001

First convert 15 to binary, then invert the bits and add 1.

Question 8

What does the Two’s Complement representation 1011 0001 signify?

Answer 8

-79

Question 9

What is the result of the left shift of 0110 1011?

Answer 9

1101 0110

Question 10

What is the effect of a left shift on a binary number?

Answer 10

We double the number

Question 11

What is the result of the right shift of 0110 1010?

Answer 11

0011 0101

Question 12

What is the effect of a right shift on a binary number?

Answer 12

We halve the number

Question 13

What happens during a further right shift?

Answer 13

We halve the number and round down, leading to a loss of precision

Question 14

What is the Two’s Complement of 0110 1010 (106)?

Answer 14

10010110 (-106)