Question

question 8 (11 points) 4 minutes using regular unsigned binary division, calculate the following: 111010010111 / 101101 enter the quotient with out any leading zeros. enter the remainder with no leading zeros.

Explanation:

Step1: Convert to decimal

The dividend \(111010010111_2\) in decimal is \(2^{11}+2^{10}+2^{9}+2^{7}+2^{4}+2^{3}+2^{1}+2^{0}=2048 + 1024+512 + 128+16 + 8+2 + 1=3735\).
The divisor \(101101_2\) in decimal is \(2^{5}+2^{3}+2^{2}+2^{0}=32 + 8+4 + 1 = 45\).

Step2: Perform decimal - division

\(3735\div45 = 83\) with a remainder of \(0\).

Step3: Convert quotient and remainder to binary

The quotient \(83\) in binary is \(1010011_2\) and the remainder \(0\) in binary is \(0\).

Answer:

Quotient: \(1010011\)
Remainder: \(0\)