Question

A convert the following Decimal numbers into Binary numbers:
a. 68
b. 987
c. 657
I want step by step solutions...​

Answer 1

Answer:

(a) 1000100

(b) 1111011011

(c) 1010010001

Explanation:

(a) Given, Decimal number is 68

Divide this number by 2 until the reminder is 0 or 1.

68/2 = 34 - Reminder 0

34/2 = 17 - Reminder 0

17/2 = 8 - Reminder 1

8/2 = 4 - Reminder 0

4/2 = 2 - Reminder 0

2/2 = 1 - Reminder 0

1 - Reminder 1

So, the binary equivalent is (68) = 1000100

(b) Given, Decimal number is 987

Divide this number by 2 until the reminder is 0 or 1.

987/2 = 493 - Reminder 1

493/2 = 246 - Reminder 1

246/2 = 123 - Reminder 0

123/2 = 61 - Reminder 1

61/2 = 30 - Reminder 1

30/2 = 15 - Reminder 0

15/2 = 7 - Reminder 1

7/2 = 3 - Reminder 1

3/2 = 1 - Reminder 1

1 - Reminder 1

So, the binary equivalent is (987) = 1111011011

(c) Given, Decimal number is 657

Divide this number by 2 until the reminder is 0 or 1.

657/2 = 328 - Reminder 1

328/2 = 164 - Reminder 0

146/2 = 82 - Reminder 0

82/2 = 41 - Reminder 0

41/2 = 20 - Reminder 1

20/2 = 10 - Reminder 0

10/2 = 5 - Reminder 0

5/2 = 2 - Reminder 1

2/2 = 1 - Reminder 0

1 - Reminder 1

So, the binary equivalent is (657) = 1010010001

Binary Numbers – Base 2

A decimal number has base 10 and a binary number has base 2. In decimal to binary conversion, the base of the number also changes, i.e. from base 10 to base 2. All the decimal numbers have its equivalent binary numbers. These binary numbers are majorly used in computer applications, where it is used for programming or coding purpose. This is because computers understand the language of binary digits, o and 1.

Hope it helps you ❤️