Binary Number

Binary numbering system uses only two symbols 0 and 1. Each digits of a binary number is referred to as bits. Binary system is also known as base -2 system. Each digit is represented by the increasing power of 2 from the LSB (Least Significant Bit). Binary system is the heart of digital electronics and is used for information flow. In digital electronics, 0 and 1 are used to denote logic states, high and low. Arithmetic operations are also possible in binary system.

Decimal Number

Whole number, a decimal point and a fractional value combines to form a decimal number. The decimal point separates the whole number part from the fractional part of the number. Each digit of a decimal number can be any number from 0 to 9. Any value less than 1 is written to the right of decimal point. Decimal numbers are also known as base-10 number or counting numbers. Place value of decimal number varies as the whole number powers of 10 starting from the left of decimal point. Similarly, the place value of digits left to decimal point varies as the division of power of tens.

How to convert a binary number to a decimal number:

Step 1:

To convert binary number to a decimal number, first of all, we have to list down each digit one below the other starting from the left.

Step 2:

Count the digit from the top to bottom. The count must start from 0.

Step 3:

Multiply each digit by 2 to the power of its position count.

Step 4:

Add all the values you calculated in the previous step. The sum gives the decimal value corresponding to the binary value.

Step 5:

Recheck your calculation.

Use Binary to Decimal convertor

Example 1:

Find the decimal value of 11010₂.

Step 1:

To convert binary number to a decimal number, first of all, we have to list down each digit one below the other starting from the left.

0
1
0
1
1

Step 2:

Count the digit from the top to bottom. The count must start from 0.

0 → position 0
1 → position 1
0 → position 2
1 → position 3
1 → position 4

Step 3:

Multiply each digit by 2 to the power of its position count.

0 → position 1    → 0 x 2⁰  = 0
1 → position 1    → 1 x 2¹  = 2
0 → position 2    → 0 x 2²  = 0
1 → position 3    → 1 x 2³  = 8
1 → position 4    → 1 x 2⁴  = 16

Step 4:

Add all the values you calculated in the previous step. The sum gives the decimal number corresponding to the binary number.

The decimal number corresponding to 11010₂ = 0 + 2 + 0 + 8 + 16 = 26

Step 5:

Recheck your calculation.

Example 2:

Find the decimal value of 100111₂.

Step 1:

To convert a binary number to a decimal number, first of all, we have to list down each digit one below the other starting from the left.

1
1
1
0
0
1

Step 2:

Count the digit from the top to bottom. The count must start from 0.

1 → position 0
1 → position 1
1 → position 2
0 → position 3
0 → position 4
1 → position 5

Step 3:

Multiply each digit by 2 to the power of its position count.

1 → position 0    → 1 x 2⁰  = 1
1 → position 1    → 1 x 2¹  = 2
1 → position 2    → 1 x 2²  = 4
0 → position 3    → 0 x 2³  = 0
0 → position 4    → 0 x 2⁴  = 0
1 → position 5    → 1 x 2⁵  = 32

Step 4:

Add all the values you calculated in the previous step. The sum gives the decimal number corresponding to the binary number.

The decimal number corresponding to 100111₂  = 1 + 2 + 4 + 0 +0 + 32 = 39

Step 5:

Recheck your calculation.

Summary

Binary number can be converted into decimal number using the following formula:

Decimal Number = (D_n X 2ⁿ + …………… + D₂ X 2² + D₁ X 2¹ + D₀ X 2⁰).

Where,

D_n – D₀ → digits of a binary number.

n  →  Position count starting from 0 (left to right).