The number 83 is written in the binary system as:

Options

A. 100110
B. 101101
C. 1010011
D. 110110

Answer

To convert the decimal number 83 into binary, we can use the method of successive division by 2 and recording the remainders. Here’s the step-by-step solution:

### Step 1: Divide 83 by 2
- **Calculation**: 83 ÷ 2 = 41 with a remainder of 1.
- **Remainder**: 1

### Step 2: Divide the quotient (41) by 2
- **Calculation**: 41 ÷ 2 = 20 with a remainder of 1.
- **Remainder**: 1

### Step 3: Divide the quotient (20) by 2
- **Calculation**: 20 ÷ 2 = 10 with a remainder of 0.
- **Remainder**: 0

### Step 4: Divide the quotient (10) by 2
- **Calculation**: 10 ÷ 2 = 5 with a remainder of 0.
- **Remainder**: 0

### Step 5: Divide the quotient (5) by 2
- **Calculation**: 5 ÷ 2 = 2 with a remainder of 1.
- **Remainder**: 1

### Step 6: Divide the quotient (2) by 2
- **Calculation**: 2 ÷ 2 = 1 with a remainder of 0.
- **Remainder**: 0

### Step 7: Divide the quotient (1) by 2
- **Calculation**: 1 ÷ 2 = 0 with a remainder of 1.
- **Remainder**: 1

### Step 8: Write the remainders in reverse order
Now, we collect all the remainders from the last division to the first:
- Remainders (from last to first): 1, 0, 1, 0, 0, 1, 1

Thus, the binary representation of the decimal number 83 is **1010011**.

### Final Answer:
The number 83 is written in the binary system as **1010011**.

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