Binary Number System

The Number system used in computers which only uses 0 and 1.

Decimal to Binary Conversion

A software engineer is writing a program that will convert decimal numbers to binary. The engineer needs to test the program with a few different numbers. What are the binary equivalents of the decimal numbers 45?

$\frac{45}{2} \implies$ Q1 = 22 & R1 = 1

$\frac{22}{2} \implies$ Q2 = 11 & R2 = 0

$\frac{11}{2} \implies$ Q3 = 5 & R3 = 1

$\frac{5}{2} \implies$ Q4 = 2 & R4 = 1

$\frac{2}{2} \implies$ Q5 = 1 & R5 = 0

$\frac{1}{2} \implies$ Q6 = 0 & R6 = 1

$\frac{0}{2} \implies$ Q7 = 0 & R7 = 0

$45_{10} = 0101101_2$

Binary to Decimal Conversion

Your grandfather gifted you a chocolate bar & your mother gave you a challenge to figure out, how much it costs ? Otherwise you can't play with that car. Your mother gave you this hint: Price amount is $1110_2$ in binary. How much rupees did it cost?

As we know the value of the car is $1110_2$ in binary, we have to convert it in decimal.

$\implies (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (0 \times 2^0)$

$\implies (1 \times 8) + (1 \times 4) + (1 \times 2) + (0 \times 1)$

$\implies 8 + 4 + 2 + 0$

$\implies 14$

Now surprise your mother by shouting 14 Rupees. Then, snatch the chocolate bar & eat it!