Problem 2E

Convert the decimal expansion of each of these integers to a binary expansion.

a) 321 b) 1023 c) 100632

Solution:

Step1

To find

Convert the decimal expansion to a binary expansion.

Step2

The decimal extension of a number is its representation in base -10.

A binary expansion is represented number in 0 or 1 .

a. 321

For binary expansion divide 321 by 2

Divide again and again by 2

Therefore, binary representation of 321 is

Step3

b. 1023

For binary expansion divide 1023 by 2

Divide again and again by 2

Therefore, binary representation of 1023 is

Step4

c)100632

For binary expansion divide 100632 by 2

Divide quotient again and again by 2

Therefore, binary representation of 100632 is