What are the last three digits from the rightend of the binary equivalent of the decimal number 5719685?

Options

A. 11
B. 110
C. 11100
D. 101

Answer

To find the last three digits from the right end of the binary equivalent of the decimal number 5719685, we will convert the decimal number to binary using repeated division by 2. Here’s the step-by-step solution:

### Step 1: Divide the number by 2
1. Start with the decimal number 5719685.
2. Divide it by 2 and record the quotient and the remainder.

\[ 5719685 \div 2 = 2859842 \quad \text{(Quotient)} \quad \text{Remainder} = 1 \]

### Step 2: Repeat the process
3. Now take the quotient (2859842) and divide it by 2.

\[ 2859842 \div 2 = 1429921 \quad \text{(Quotient)} \quad \text{Remainder} = 0 \]

4. Take the new quotient (1429921) and divide it by 2.

\[ 1429921 \div 2 = 714960 \quad \text{(Quotient)} \quad \text{Remainder} = 1 \]

### Step 3: Continue until the quotient is 0
5. Continue this process until the quotient becomes 0, recording the remainders:

\[ 714960 \div 2 = 357480 \quad \text{Remainder} = 0 \]
\[ 357480 \div 2 = 178740 \quad \text{Remainder} = 0 \]
\[ 178740 \div 2 = 89370 \quad \text{Remainder} = 0 \]
\[ 89370 \div 2 = 44685 \quad \text{Remainder} = 0 \]
\[ 44685 \div 2 = 22342 \quad \text{Remainder} = 1 \]
\[ 22342 \div 2 = 11171 \quad \text{Remainder} = 0 \]
\[ 11171 \div 2 = 5585 \quad \text{Remainder} = 1 \]
\[ 5585 \div 2 = 2792 \quad \text{Remainder} = 1 \]
\[ 2792 \div 2 = 1396 \quad \text{Remainder} = 0 \]
\[ 1396 \div 2 = 698 \quad \text{Remainder} = 0 \]
\[ 698 \div 2 = 349 \quad \text{Remainder} = 0 \]
\[ 349 \div 2 = 174 \quad \text{Remainder} = 1 \]
\[ 174 \div 2 = 87 \quad \text{Remainder} = 0 \]
\[ 87 \div 2 = 43 \quad \text{Remainder} = 1 \]
\[ 43 \div 2 = 21 \quad \text{Remainder} = 1 \]
\[ 21 \div 2 = 10 \quad \text{Remainder} = 1 \]
\[ 10 \div 2 = 5 \quad \text{Remainder} = 0 \]
\[ 5 \div 2 = 2 \quad \text{Remainder} = 1 \]
\[ 2 \div 2 = 1 \quad \text{Remainder} = 0 \]
\[ 1 \div 2 = 0 \quad \text{Remainder} = 1 \]

### Step 4: Collect the remainders
6. Now, collect all the remainders starting from the last division to the first. The binary equivalent of 5719685 is:

\[ 1010111101110001101011101 \]

### Step 5: Identify the last three digits
7. The last three digits from the right end of the binary number are:

\[ 101 \]

### Final Answer
The last three digits from the right end of the binary equivalent of the decimal number 5719685 are **101**.

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