In a binary number system, assume that a=00111 and b=01110, then in a decimal system `(b)/(a)`, which is equal to

Options

A. 1
B. 2
C. 4
D. 5

Explanation

To solve the problem of finding \( \frac{b}{a} \) in a decimal system where \( a = 00111 \) and \( b = 01110 \) in binary, we will follow these steps:

### Step 1: Convert \( a \) from binary to decimal
The binary number \( a = 00111 \) can be converted to decimal by calculating the sum of powers of 2 for each bit that is set to 1.

- The binary representation is:
- \( 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 \)

Calculating this gives:
- \( 0 + 0 + 4 + 2 + 1 = 7 \)

Thus, \( a = 7 \) in decimal.

### Step 2: Convert \( b \) from binary to decimal
The binary number \( b = 01110 \) can also be converted to decimal in a similar manner.

- The binary representation is:
- \( 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 \)

Calculating this gives:
- \( 0 + 8 + 4 + 2 + 0 = 14 \)

Thus, \( b = 14 \) in decimal.

### Step 3: Calculate \( \frac{b}{a} \)
Now that we have both \( a \) and \( b \) in decimal, we can calculate \( \frac{b}{a} \):

\[ \frac{b}{a} = \frac{14}{7} = 2 \]

### Final Answer
The value of \( \frac{b}{a} \) in decimal is \( 2 \).

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