The number 251 in decimal system is expressed in binary system by:

Options

A. (A)11110111
B. (B)`11111011`
C. (C)`11111101`
D. (D)`11111110`

Answer

To convert the decimal number 251 into binary, we can use the division method. Here’s a step-by-step solution:

### Step 1: Divide the number by 2
- **Operation**: 251 ÷ 2
- **Quotient**: 125
- **Remainder**: 1

### Step 2: Divide the quotient by 2
- **Operation**: 125 ÷ 2
- **Quotient**: 62
- **Remainder**: 1

### Step 3: Divide the new quotient by 2
- **Operation**: 62 ÷ 2
- **Quotient**: 31
- **Remainder**: 0

### Step 4: Divide the new quotient by 2
- **Operation**: 31 ÷ 2
- **Quotient**: 15
- **Remainder**: 1

### Step 5: Divide the new quotient by 2
- **Operation**: 15 ÷ 2
- **Quotient**: 7
- **Remainder**: 1

### Step 6: Divide the new quotient by 2
- **Operation**: 7 ÷ 2
- **Quotient**: 3
- **Remainder**: 1

### Step 7: Divide the new quotient by 2
- **Operation**: 3 ÷ 2
- **Quotient**: 1
- **Remainder**: 1

### Step 8: Divide the new quotient by 2
- **Operation**: 1 ÷ 2
- **Quotient**: 0
- **Remainder**: 1

### Step 9: Collect the remainders
Now, we collect all the remainders from the last division to the first:
- Remainders (from last to first): 1, 1, 1, 1, 1, 0, 1

### Step 10: Write the binary number
The binary representation of the decimal number 251 is:
- **Binary**: 11111011

Thus, the number 251 in decimal system is expressed in binary system as **11111011**.

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