Convert 111 Binary to Decimal

111 binary to decimal conversion provides the detailed information on what is binary (111)2 in decimal number system, and the step-by-step work for how to convert the binary (base-2) number 111 to its decimal (base-10) equivalent.

(111)₂ binary in decimal is equal to:
111₂ = (1 x 2²) + (1 x 2¹) + (1 x 2⁰)
= 4 + 2 + 1,
= 7
111₂ = 7₁₀

Hence,
111 binary to decimal is 7.

where,
111₂ is the given binary number,
2 in 111₂ represents the base-2 or binary number system,
7 is the decimal equivalent of the binary number 111,
10 in 7₁₀ represents the base-10 or decimal number system.

Steps to convert 111 binary to decimal
The below step-by-step solution shows how to convert 111101 binary (base 2) to its equivalent decimal (base 10) number.

step 1 Observe the input parameters, values and what to be found.

Input values:
Binary Number = 111₂

What to be found:
(111)₂ = (?)₁₀
What is 111 binary in decimal?

step 2 Arrange the given binary number 111 as like the below:
= (1 x 2²) + (1 x 2¹) + (1 x 2⁰),

step 3 Resolve the powers of 2 in the above equation:
= 4 + 2 + 1,

step 3 Simplify the above equation further:
= 4 + 2 + 1,
= 7
(111)₂ = (7)₁₀

Therefore,
the decimal equivalent of the binary number 111 is 7

Important Notes: (111)2 in Decimal
The below are some of the important notes to be remembered while converting the binary number 111 into a base-10 number.

The sum of increasing power of 2 (from 0 to number of bits minus 1) for each bit of given binary number 111, that is 2⁰ multiplied with least significant digit (LSD) to 2(no. of bits - 1) multiplied with the most significant digit (MSD) of the given base-2 number provides the equivalent decimal number.

1. The right most digit in the given base-2 number 111 is a Least Significant Bit (LSB).
2. The left most digit in the given base-2 number 111 is a Most Significant Bit (MSB).
3. The LSB of 111 should be multiplied with 2⁰.
4. The MSB of 111 should be multiplied with 2^{(no. of bits - 1)}.