Question

How do you convert binary to decimal number?

Answer 1

Step 1: Conversion of binary to decimal number.

As we know that,

A binary number is a number made up of $0s$ and $1s$ bits that represents information or data saved in a computer. Because it has two bits, $0s$ and $1s$, it is also known as the base $2$ numeral system. $1001,1010,1101,1111,1010101$, and so on are binary numbers $(0and1)$.

A decimal number is one with ten digits ranging from $0$ to $9$. Its basis is ten since it collects ten digits $(0,1,2,3,4,5,6,7,8,9)$ and uses these ten digits to represent or construct the complete number.

Step 2: Method for Binary to Decimal Conversion

Converting a number in a binary number system (base$-2$) to a number in a decimal number system is known as binary to decimal conversion (base-$10$). The multiplication method is used to convert a binary number to a decimal value.

1. From right to left, write the supplied binary number and count the powers of $2$ (powers starting from $0$)
2. Multiply the first binary digit (MSB) by the biggest power of $2$ from right to left.
3. Combine all of the products from the previous step.
4. The required decimal number will be the final solution.

Step 3: Formula for conversion of Binary to Decimal.

We will find the decimal number from the binary number by using the following formula is,

$Decimalnumber=n^{th}bit\times 2^{n-1}$

$n=b_n{q}^n+b_{n-1}{q}^{n-2}+...+b_2{q}^2+b_1{q}^1+b_0{q}^0+b_{-1}{q}^{-1}+b_{-2}{q}^{-2}$

here, $n$ is the decimal equivalent, $b$ is the digit and $q$ is the base value.

For example,

Find the decimal value of ${111001}_2$.

Binary number	1	1	1	0	0	1
Power of 2	$2^5$	$2^4$	$2^3$	$2^2$	$2^1$	$2^0$

$\Rightarrow$ ${111001}_2=1.2^5+1.2^4+1.2^3+0.2^2+0.2^1+1.2^0$

$\Rightarrow$ ${111001}_2={57}_{10}$

Hence, we can convert binary to decimal number by using the formula,

$n=b_n{q}^n+b_{n-1}{q}^{n-2}+...+b_2{q}^2+b_1{q}^1+b_0{q}^0+b_{-1}{q}^{-1}+b_{-2}{q}^{-2}$.