Binary to Decimal converter

How to convert binary to decimal

For binary number with n digits:

d_n-1 ... d₃ d₂ d₁ d₀

So decimal number is equal to the sum of binary digits (d_n) times their power of 2 (2ⁿ).

decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + ...

Example 1

Find the decimal value of 111011₂:

binary number:	1	1	1	0	1	1
power of 2:	2⁵	2⁴	2³	2²	2¹	2⁰

(111011)₂ = (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (59)₁₀

Example 2

Find the decimal value of 110011₂:

binary number:	1	1	0	0	1	1
power of 2:	2⁵	2⁴	2³	2²	2¹	2⁰

(110011)₂ = (1 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (51)₁₀

Example 3

Find the decimal value of 101011₂:

binary number:	1	0	1	0	1	1
power of 2:	2⁵	2⁴	2³	2²	2¹	2⁰

(101011)₂ = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (43)₁₀

Binary to decimal conversion table

Binary Number	Decimal Number	Hex Number
0	0	0
1	1	1
10	2	2
11	3	3
100	4	4
101	5	5
110	6	6
111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F
10000	16	10
10001	17	11
10010	18	12
10011	19	13
10100	20	14
10101	21	15
10110	22	16
10111	23	17
11000	24	18
11001	25	19
11010	26	1A
11011	27	1B
11100	28	1C
11101	29	1D
11110	30	1E
11111	31	1F
100000	32	20
1000000	64	40
10000000	128	80
100000000	256	100

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