Convert the following decimal numbers to binary: 6. 5 = 7. 18 = 8. 31 = 9. 45 = 101101 10. 63 =

To convert decimal numbers to binary, you need to repeatedly divide the number by 2 and record the remainder. The binary representation is obtained by writing down the remainders in reverse order.

6 :

Divide by 2: 6 ÷ 2 = 3, remainder 0
Divide by 2: 3 ÷ 2 = 1, remainder 1
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 6 in binary is 110 .

7 :

Divide by 2: 7 ÷ 2 = 3, remainder 1
Divide by 2: 3 ÷ 2 = 1, remainder 1
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 7 in binary is 111 .

18 :

Divide by 2: 18 ÷ 2 = 9, remainder 0
Divide by 2: 9 ÷ 2 = 4, remainder 1
Divide by 2: 4 ÷ 2 = 2, remainder 0
Divide by 2: 2 ÷ 2 = 1, remainder 0
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 18 in binary is 10010 .

31 :

Divide by 2: 31 ÷ 2 = 15, remainder 1
Divide by 2: 15 ÷ 2 = 7, remainder 1
Divide by 2: 7 ÷ 2 = 3, remainder 1
Divide by 2: 3 ÷ 2 = 1, remainder 1
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 31 in binary is 11111 .

45 :

Divide by 2: 45 ÷ 2 = 22, remainder 1
Divide by 2: 22 ÷ 2 = 11, remainder 0
Divide by 2: 11 ÷ 2 = 5, remainder 1
Divide by 2: 5 ÷ 2 = 2, remainder 1
Divide by 2: 2 ÷ 2 = 1, remainder 0
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 45 in binary is 101101 .

63 :

Divide by 2: 63 ÷ 2 = 31, remainder 1
Divide by 2: 31 ÷ 2 = 15, remainder 1
Divide by 2: 15 ÷ 2 = 7, remainder 1
Divide by 2: 7 ÷ 2 = 3, remainder 1
Divide by 2: 3 ÷ 2 = 1, remainder 1
Divide by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders backward, 63 in binary is 111111 .


These are the binary equivalents of the given decimal numbers.

Answered by LucasMatthewHarris | 2025-07-21