Question

The remainder and the quotient of the binary division $(101110{)}_2÷(110{)}_2$ are respectively

• A. $(111{)}_2$ and $(100{)}_2$
• B. $(100{)}_2$ and $(111{)}_2$
• C. $(101{)}_2$ and $(101{)}_2$
• D. $(100{)}_2$ and $(100{)}_2$

Answer 1

The correct option is B $(100{)}_2$ and $(111{)}_2$

Converting the binary system to decimal system, we get

${101110}_2=2+4+8+32=46$ and ${110}_2=2+4=6$

$⟹46÷6$ gives,

The quotient is $7$ and remainder is $4$

Converting them back to binary again, we get

quotient is ${111}_2$ and remainder is ${100}_2$

Hence, the answer is $(100{)}_2$ and $(111{)}_2$.