Question

Divide 101011 by 1001 and check the result by converting to decimal system. Also, write quotient and remainder.​

Answer 1

Given:

Dividend = (101011)₂ = (43)₁₀

Divisor = (1001)₂ = (9)₁₀

To find:

Divide 101011 by 1001 and check the result by converting to the decimal system. Also, write quotient and remainder.​

Solution:

        10      

1001) 101011

      - 1001↓↓

               111

             - 000

                111  

Quotient = (10)₂ = (2)₁₀

Remainder = (111)₂ = (7)₁₀

Verification:

Dividend = Divisor × Quotient + Remainder

Dividend = 9 × 2 + 7

Dividend = 36 + 7

Dividend = 43

Since we get the same value of the dividend.

Hence verified

Conversion of the binary system to decimal system:

101011

1    0    1    0    1     1

×    ×    ×    ×    ×    ×

2⁵  2⁴  2³  2²   2¹   2⁰

= 2⁵ + 2³ + 2¹ + 2⁰

= 32 + 8 + 2 + 1

= 43

So, (101011)₂ = (43)₁₀

Similarly, we can do for the remaining.