Question

Using arithmetic shifting, perform the following:

a)double the value 000101012
b)quadruple the value 011101112
c)divide the value 110010102in half

Answer 1

Arithmetic shifting involves multiplying or dividing a number by powers of 2 using specific rules. To double a number using arithmetic shifting, shift all the digits to the left and add a 0 to the right. To quadruple a number, shift all the digits to the left twice and add two 0s to the right. To divide a number in half, shift all the digits to the right.

Step-by-step explanation:

When performing arithmetic shifting, we can use the rules provided as reference:

1. a. The value will increase by a factor of two.
2. b. The value will increase by a factor of four.
3. c. The value will increase by a factor of six.
4. d. The value will increase by a factor of eight.

So, using arithmetic shifting:

1. a. To double the value 00010101, we shift all the digits to the left and add a 0 to the right: 00010101 becomes 00101010, which is double the original value.
2. b. To quadruple the value 01110111, we shift all the digits to the left and add a 0 to the right: 01110111 becomes 11101110, which is four times the original value.
3. c. To divide the value 11001010 in half, we shift all the digits to the right: 11001010 becomes 01100101, which is half the original value.