Binary Quiz: How To Count In Binary?

Explanation
The correct answer is: 00011110To convert the decimal number 30 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 30 by 2:30 ÷ 2 = 15 remainder 0(Least significant bit: 0)Divide 15 by 2:15 ÷ 2 = 7 remainder 1(Next bit: 1)Divide 7 by 2:7 ÷ 2 = 3 remainder 1(Next bit: 1)Divide 3 by 2:3 ÷ 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00011110So, the binary representation of 30 is 00011110.

Explanation
The correct answer is: 00101000To convert the decimal number 40 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 40 by 2:40 ÷ 2 = 20 remainder 0(Least significant bit: 0)Divide 20 by 2:20 ÷ 2 = 10 remainder 0(Next bit: 0)Divide 10 by 2:10 ÷ 2 = 5 remainder 0(Next bit: 0)Divide 5 by 2:5 ÷ 2 = 2 remainder 1(Next bit: 1)Divide 2 by 2:2 ÷ 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00101000So, the binary representation of 40 is 00101000.

Explanation
The correct answer is: 00110111To convert the decimal number 55 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 55 by 2:55 ÷ 2 = 27 remainder 1(Least significant bit: 1)Divide 27 by 2:27 ÷ 2 = 13 remainder 1(Next bit: 1)Divide 13 by 2:13 ÷ 2 = 6 remainder 1(Next bit: 1)Divide 6 by 2:6 ÷ 2 = 3 remainder 0(Next bit: 0)Divide 3 by 2:3 ÷ 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00110111So, the binary representation of 55 is 00110111.

Explanation
To convert the decimal number 63 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 63 by 2:63 ÷ 2 = 31 remainder 1(Least significant bit: 1)Divide 31 by 2:31 ÷ 2 = 15 remainder 1(Next bit: 1)Divide 15 by 2:15 ÷ 2 = 7 remainder 1(Next bit: 1)Divide 7 by 2:7 ÷ 2 = 3 remainder 1(Next bit: 1)Divide 3 by 2:3 ÷ 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00111111So, the binary representation of 63 is 00111111.

Explanation
The correct answer is: 01001110To convert the decimal number 78 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 78 by 2:78 ÷ 2 = 39 remainder 0(Least significant bit: 0)Divide 39 by 2:39 ÷ 2 = 19 remainder 1(Next bit: 1)Divide 19 by 2:19 ÷ 2 = 9 remainder 1(Next bit: 1)Divide 9 by 2:9 ÷ 2 = 4 remainder 1(Next bit: 1)Divide 4 by 2:4 ÷ 2 = 2 remainder 0(Next bit: 0)Divide 2 by 2:2 ÷ 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 01001110So, the binary representation of 78 is 01001110.

Explanation
The correct binary representation of 90 is 1011010.To convert the decimal number 90 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 90 by 2:90 ÷ 2 = 45 remainder 0(Least significant bit: 0)Divide 45 by 2:45 ÷ 2 = 22 remainder 1(Next bit: 1)Divide 22 by 2:22 ÷ 2 = 11 remainder 0(Next bit: 0)Divide 11 by 2:11 ÷ 2 = 5 remainder 1(Next bit: 1)Divide 5 by 2:5 ÷ 2 = 2 remainder 1(Next bit: 1)Divide 2 by 2:2 ÷ 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 1011010So, the binary representation of 90 is 1011010.

Explanation
The correct answer is: 01101001To convert the decimal number 105 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 105 by 2:105 ÷ 2 = 52 remainder 1(Least significant bit: 1)Divide 52 by 2:52 ÷ 2 = 26 remainder 0(Next bit: 0)Divide 26 by 2:26 ÷ 2 = 13 remainder 0(Next bit: 0)Divide 13 by 2:13 ÷ 2 = 6 remainder 1(Next bit: 1)Divide 6 by 2:6 ÷ 2 = 3 remainder 0(Next bit: 0)Divide 3 by 2:3 ÷ 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 01101001So, the binary representation of 105 is 01101001.

Explanation
The correct answer is: 10000000To convert the decimal number 128 into binary, you can use repeated division by 2 and keep track of the remainders. However, in this case, it is important to note that 128 is a power of 2 (2^7), so its binary representation will have only one '1' followed by seven '0's.So, the binary representation of 128 is 10000000.

Explanation
The correct answer is: 10011100To convert the decimal number 156 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 156 by 2:156 ÷ 2 = 78 remainder 0(Least significant bit: 0)Divide 78 by 2:78 ÷ 2 = 39 remainder 0(Next bit: 0)Divide 39 by 2:39 ÷ 2 = 19 remainder 1(Next bit: 1)Divide 19 by 2:19 ÷ 2 = 9 remainder 1(Next bit: 1)Divide 9 by 2:9 ÷ 2 = 4 remainder 1(Next bit: 1)Divide 4 by 2:4 ÷ 2 = 2 remainder 0(Next bit: 0)Divide 2 by 2:2 ÷ 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 ÷ 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 10011100So, the binary representation of 156 is 10011100.

Explanation
To convert a decimal number into a binary number, we divide the decimal number by 2 repeatedly and record the remainders. Starting with 199, we divide it by 2 to get a quotient of 99 and a remainder of 1. We then divide 99 by 2 to get a quotient of 49 and a remainder of 1. Continuing this process, we divide 49 by 2 to get a quotient of 24 and a remainder of 1. We divide 24 by 2 to get a quotient of 12 and a remainder of 0. We divide 12 by 2 to get a quotient of 6 and a remainder of 0. We divide 6 by 2 to get a quotient of 3 and a remainder of 0. Finally, we divide 3 by 2 to get a quotient of 1 and a remainder of 1. The binary representation of 199 is therefore 11000111.