Divide in binary a. 11101001 ÷ 110 b. 110000001 ÷ 1110
The correct answer and explanation is:
a. 11101001 ÷ 110
Step 1: Convert the binary numbers to decimal for easy understanding.
- 11101001 (binary) = 1 × 2^7 + 1 × 2^6 + 1 × 2^5 + 0 × 2^4 + 1 × 2^3 + 0 × 2^2 + 0 × 2^1 + 1 × 2^0 = 233 (decimal)
- 110 (binary) = 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 6 (decimal)
Step 2: Perform the division in decimal.
- 233 ÷ 6 = 38 remainder 5
Step 3: Convert the quotient and remainder back to binary.
- 38 in decimal = 100110 (binary)
- 5 in decimal = 101 (binary)
Thus, 11101001 ÷ 110 = 100110 remainder 101 (binary).
b. 110000001 ÷ 1110
Step 1: Convert the binary numbers to decimal.
- 110000001 (binary) = 1 × 2^8 + 1 × 2^7 + 0 × 2^6 + 0 × 2^5 + 0 × 2^4 + 0 × 2^3 + 0 × 2^2 + 0 × 2^1 + 1 × 2^0 = 385 (decimal)
- 1110 (binary) = 1 × 2^3 + 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 14 (decimal)
Step 2: Perform the division in decimal.
- 385 ÷ 14 = 27 remainder 5
Step 3: Convert the quotient and remainder back to binary.
- 27 in decimal = 11011 (binary)
- 5 in decimal = 101 (binary)
Thus, 110000001 ÷ 1110 = 11011 remainder 101 (binary).
Explanation of the Process:
- Converting Binary to Decimal: We first convert the binary numbers to decimal so that we can perform simple division. This involves breaking down each binary number into its constituent powers of 2 and then summing them up.
- Performing the Division in Decimal: After converting both the dividend and divisor to decimal, we divide the two numbers in the usual way to find the quotient and remainder.
- Converting the Result Back to Binary: Finally, the quotient and remainder from the division are converted back to binary form for the final result.
This method can be used for binary division by first simplifying the operation to a more familiar decimal form and then converting the result back to binary.