Question

The Decimal number 605 in binary will be:
A. 100101
B. 10010111
C. 1001011101
D. 100101101

Answer 1

Hint:-
The decimal number is divided by 2. The integer quotient is obtained for the next iteration. The remainder will be kept for the binary digit. The following steps are repeated until the quotient is equal to 0. Finally, the binary number is written from the last remainder to the first remainder.

Complete step-by-step solution :Decimal number is the most familiar number system to the general public. It is base 10 which has only 10 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Whereas Binary number is the most familiar number system to the digital systems, networking, and computer professionals. It is base 2 which has only 2 symbols: 0 and 1, these digits can be represented by off and on respectively.

The steps algorithm is followed for conversion of decimal number to binary number.
Take the decimal number as dividend.
Divide this number by 2 (2 is base of binary so divisor here).
Store the remainder in an array (it will be either 0 or 1 because of divisor 2).
Repeat the above two steps until the number is greater than zero.
Print the array in reverse order (which will be equivalent to the binary number of the given decimal number).
Last remainder will be MSB (Most Significant Bit) and the first remainder will be LSB (Least Significant

DIVISOR	DIVIDEND	REMAINDER
2	605
2	302	1
2	151	0
2	75	1
2	37	1
2	18	1
2	9	0
2	4	1
2	2	0
2	1	0
2	0	1

Bit).
Given, the decimal number is 605.

Now, writing all the remainders from last to first, we get: (1001011101)
Thus, we obtained conversion of decimal number to binary number, as follows:
$$$$$\therefore {\left( {605} \right)_{10}} = {\left( {1001011101} \right)_2}$

Note:-
Any decimal number can be converted to an equivalent binary number by repeated division by 2 for ‘integers’ and repeated multiplication by 2 for fractions.