Question

I don't understand this at all.
Please help!!!
Thank you. ​

Answer 1

Topic

• Binary

Binary is a number system of base 2. Digits of binary consist of 0 and 1. Digit by digit, the exponent of the base grows by 1.

Example) $1_{(2)}=1$, $10_{(2)}=2$, $100_{(3)}=4$, ….

Since the question is giving $*$ and $\bullet$ as digits, the given number system is binary.

For example, 4 is 100₍₂₎ in binary. So it will be $\bullet\ *\ *$ in the given form.

Solution

43. $\bullet\ \bullet\ \bullet$ is added to $\bullet\ *\ *$.

⇒ $111_{(2)}$ is added to $100_{(2)}$.

$\implies 111_{(2)}+100_{(2)}=1011_{(2)}$

⇒ (b) $\bullet\ *\ \bullet\ \bullet$ is the required option.

44. Which binary number represents 15?

Via the repeated division by 2 method, we find the number in the binary form.

$\implies 15=1111_{(2)}$

⇒ (c) $\bullet\ \bullet\ \bullet\ \bullet$ is the required option.

45. If $11100_{(2)}$ is divided by $111_{(2)}$, we are dividing $28$ by $7$ of decimal.

$\implies 4=100_{(2)}$

⇒ (a) $\bullet\ *\ *$ is the required option.

46. Which number represents 20?

$\implies 20=10100_{(2)}$

⇒ (d) $\bullet\ *\ \bullet\ *\ *$ is the required option.

47. Which number represents 15% of 80?

Firstly, in decimal, the required number is $80\times \dfrac{15}{100} =12$.

Via the repeated division method, we find $12$ in the binary form.

$\implies 12=1100_{(2)}$

⇒ (b) $\bullet\ \bullet\ *\ *$ is the required option.

More Information

In the repeated division by 2 method, we use the remainder and the last quotient. The name is because of dividing the quotient repeatedly by 2.