Solved on Feb 23, 2024

What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

STEP 1

Assumptions
1. We need to convert the decimal number 12 into its binary equivalent.
2. Binary numbers are represented using only two digits: 0 and 1.
3. The place values in binary are powers of 2, starting from the rightmost digit which is $2^0$ , then $2^1$ , $2^2$ , $2^3$ , and so on.

STEP 2

To convert the decimal number 12 to binary, we will divide the number by 2 and record the remainder. This process will be repeated with the quotient until the quotient is 0.
$12 \div 2 = 6 \quad \text{with remainder} \quad 0$

STEP 3

Now divide the quotient from the previous step by 2 and record the remainder.
$6 \div 2 = 3 \quad \text{with remainder} \quad 0$

STEP 4

Repeat the division for the new quotient.
$3 \div 2 = 1 \quad \text{with remainder} \quad 1$

STEP 5

Finally, divide the last quotient by 2.
$1 \div 2 = 0 \quad \text{with remainder} \quad 1$

STEP 6

Now that we have reached a quotient of 0, we will write down the remainders in reverse order to get the binary representation of the decimal number 12.
The remainders from the last to the first are: $1, 1, 0, 0$ .

STEP 7

The binary value of the decimal number 12 is therefore $1100$ .
The correct answer is b. $1100$ .

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What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

STEP 1

Assumptions
1. We need to convert the decimal number 12 into its binary equivalent.
2. Binary numbers are represented using only two digits: 0 and 1.
3. The place values in binary are powers of 2, starting from the rightmost digit which is $2^0$ , then $2^1$ , $2^2$ , $2^3$ , and so on.

STEP 2

To convert the decimal number 12 to binary, we will divide the number by 2 and record the remainder. This process will be repeated with the quotient until the quotient is 0.
$12 \div 2 = 6 \quad \text{with remainder} \quad 0$

STEP 3

Now divide the quotient from the previous step by 2 and record the remainder.
$6 \div 2 = 3 \quad \text{with remainder} \quad 0$

STEP 4

Repeat the division for the new quotient.
$3 \div 2 = 1 \quad \text{with remainder} \quad 1$

STEP 5

Finally, divide the last quotient by 2.
$1 \div 2 = 0 \quad \text{with remainder} \quad 1$

STEP 6

Now that we have reached a quotient of 0, we will write down the remainders in reverse order to get the binary representation of the decimal number 12.
The remainders from the last to the first are: $1, 1, 0, 0$ .

STEP 7

The binary value of the decimal number 12 is therefore $1100$ .
The correct answer is b. $1100$ .

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What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

STEP 1

Assumptions1. We need to convert the decimal number 12 into its binary equivalent.2. Binary numbers are represented using only two digits: 0 and 1.3. The place values in binary are powers of 2, starting from the rightmost digit which is 202^020, then 212^121, 222^222, 232^323, and so on.

STEP 2

To convert the decimal number 12 to binary, we will divide the number by 2 and record the remainder. This process will be repeated with the quotient until the quotient is 0.12÷2=6with remainder012 \div 2 = 6 \quad \text{with remainder} \quad 012÷2=6with remainder0

STEP 3

Now divide the quotient from the previous step by 2 and record the remainder.6÷2=3with remainder06 \div 2 = 3 \quad \text{with remainder} \quad 06÷2=3with remainder0

STEP 4

Repeat the division for the new quotient.3÷2=1with remainder13 \div 2 = 1 \quad \text{with remainder} \quad 13÷2=1with remainder1

STEP 5

Finally, divide the last quotient by 2.1÷2=0with remainder11 \div 2 = 0 \quad \text{with remainder} \quad 11÷2=0with remainder1

STEP 6

Now that we have reached a quotient of 0, we will write down the remainders in reverse order to get the binary representation of the decimal number 12.The remainders from the last to the first are: 1,1,0,01, 1, 0, 01,1,0,0.

STEP 7

The binary value of the decimal number 12 is therefore 110011001100.The correct answer is b. 110011001100.

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Assumptions
1. We need to convert the decimal number 12 into its binary equivalent.
2. Binary numbers are represented using only two digits: 0 and 1.
3. The place values in binary are powers of 2, starting from the rightmost digit which is $2^0$ , then $2^1$ , $2^2$ , $2^3$ , and so on.

To convert the decimal number 12 to binary, we will divide the number by 2 and record the remainder. This process will be repeated with the quotient until the quotient is 0.
$12 \div 2 = 6 \quad \text{with remainder} \quad 0$

Now divide the quotient from the previous step by 2 and record the remainder.
$6 \div 2 = 3 \quad \text{with remainder} \quad 0$

Repeat the division for the new quotient.
$3 \div 2 = 1 \quad \text{with remainder} \quad 1$

Finally, divide the last quotient by 2.
$1 \div 2 = 0 \quad \text{with remainder} \quad 1$

Now that we have reached a quotient of 0, we will write down the remainders in reverse order to get the binary representation of the decimal number 12.
The remainders from the last to the first are: $1, 1, 0, 0$ .

The binary value of the decimal number 12 is therefore $1100$ .
The correct answer is b. $1100$ .