To divide the binary number (011010000) by (0101), we need to perform binary division. Let's go through the steps to find the quotient.

Step 1: Set up the division
Write the dividend and divisor in binary format, aligning them properly:

10010 (dividend)
/0101 (divisor)

Step 2: Perform the first division
Start by dividing the leftmost digits of the dividend (01) by the leftmost digit of the divisor (0). Since we cannot divide 1 by 0, we bring down the next digit (1) from the dividend.

10010 (dividend)
/0101 (divisor)
-

101 (new dividend)

Step 3: Perform the second division
Now, we divide the new dividend (101) by the divisor (0101).

10010 (dividend)
/0101 (divisor)
- 1001
----
101

Since the divisor is larger than the new dividend, we bring down the next digit (0) from the original dividend.

Step 4: Perform the third division
We now divide the new dividend (1010) by the divisor (0101).

10010 (dividend)
/0101 (divisor)
- 1001
----
1010
- 1010
----
0

Since the new dividend is now zero, we stop the division process.

Step 5: Determine the quotient
The quotient is obtained by combining the remainders from each division step. In our case, the remainders are 1001 and 1010, which gives us the binary quotient: 10011010.

Step 6: Convert the quotient to decimal
To convert the binary quotient to decimal, we can use the positional notation. Starting from the rightmost digit, we assign powers of 2 to each digit and sum them up:

1 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 128 + 16 + 8 + 2 = 154

Therefore, the quotient of (011010000) divided by (0101) is 10011010 in binary or 154 in decimal.

The correct answer is option 'B' (101001).