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Binary to Decimal Converter

To use binary to decimal converter, type a binary value e.g. "1110" and click on the Convert button and you will get the decimal value of 14 on the right side. The binary to decimal conversion table for values up to 255 is shown below.

Binary value

Decimal value

Binary to Decimal Conversion:

Decimal = 14

Binary Numeral System
Decimal Numeral System
How to Convert Binary to Decimal
How to Convert Binary Fraction to Decimal
FAQs (Binary to Decimal Conversion)
Binary to Decimal Table

Binary Numeral System

The binary number system is a way of representing numbers using only two symbols: 0 and 1, with base 2 as its radix. In the digital world, computers are entirely built on the binary system. Every piece of information, from text to images, is converted into binary code for processing. Numbers are expressed as powers of 2, such as 2⁰, 2¹, 2², and so forth. Each individual binary digit is called a bit, and a collection of 8 bits forms a Byte.

Example:

Binary value (1100.101)₂ is equal to decimal number (12.625)₁₀. It can be represented as powers to the base 2:

Digit	Position	Power of 2	Value
1	2³ (Eights place)	2³ = 8	1 × 8 = 8
1	2² (Fours place)	2² = 4	1 × 4 = 4
0	2¹ (Twos place)	2¹ = 2	0 × 2 = 0
0	2⁰ (Ones place)	2⁰ = 1	0 × 1 = 0
1	2^-1 (Halves place)	2^-1 = 0.5	1 × 0.5 = 0.5
0	2^-2 (Quarters place)	2^-2 = 0.25	0 × 0.25 = 0
1	2^-3 (Eighths place)	2^-3 = 0.125	1 × 0.125 = 0.125

(1100.101)₂ = (1 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰) + (1 × 2^-1) + (0 × 2^-2) + (1 × 2^-2) = (8 + 4 + 0.5 + 0.125) = (12.625)₁₀ (Decimal)

Decimal Numeral System

The decimal system is built on base 10, meaning it relies on ten unique symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This base-10 structure is the standard method used worldwide to represent both whole numbers and fractions. Each digit in a decimal number is assigned a value according to powers of 10 (10⁰, 10¹, 10², 10^-1, etc.).

Decimal number "6945.395" can be expressed as powers of 10:

Digit	Position	Power of 10	Value
6	10³ (Thousands place)	10³ = 1000	6 × 1000 = 6000
9	10² (Hundreds place)	10² = 100	9 × 100 = 900
4	10¹ (Tens place)	10¹ = 10	4 × 10 = 40
5	10⁰ (Ones place)	10⁰ = 1	5 × 1 = 5
3	10^-1 (Tenths place)	10^-1 = 0.1	3 × 0.1 = 0.3
9	10^-2 (Hundredths place)	10^-2 = 0.01	9 × 0.01 = 0.09
5	10^-3 (Thousandths place)	10^-3 = 0.001	5 × 0.001 = 0.005

Total = (6 × 10³) + (9 × 10²) + (4 × 10¹) + (5 × 10⁰) + (3 × 10^-1) + (9 × 10^-2) + (5 × 10^-3) = 6000 + 900 + 40 + 5 + 0.3 + 0.09 + 0.005 = 6945.395

How to Convert Binary to Decimal

There are two ways to convert a binary number to a decimal equivalent. First is the position based approach which is described in the above example. The second method is called the double dabble algorithm or shift-and-add-3 algorithm.

Method-1: Position Based Approach

In this approach, there are two steps to convert a binary number to a decimal.

Step-1: Represent the bits of binary number as powers to the base 2, from the Least Significant Bit (LSB - rightmost bit) position to the Most Significant Bit (MSB - leftmost bit).
Step-2: Multiply the bits values to the powers to the base 2 and add the results.

How to Convert Binary Fraction to Decimal Value

Follow these steps to convert fractional binary value to a decimal:

Step-1: Get the fractional value from the binary number (101.110) e.g. 110 is the fractional part.
Step-2: Multiply each bit by 2^-n where n starts at 1 for the first digit after the binary point and increases rightward. For example, the first bit 1 is multiplied by 2^-1, the next bit 1 is multiplied by 2^-2 and so on.
Step-3: Add the results to get the fractional part of the final decimal value.

Example 1: Convert (100010)₂ to decimal.

Bits	Position	Power of 2	Value
1	2⁵ (32’s place)	2⁵ = 32	1 × 32 = 32
0	2⁴ (16’s place)	2⁴ = 16	0 × 16 = 0
0	2³ (8’s place)	2³ = 8	0 × 8 = 0
0	2² (4’s place)	2² = 4	0 × 4 = 0
1	2¹ (2’s place)	2¹ = 2	1 × 2 = 2
0	2⁰ (1’s place)	2⁰ = 1	0 × 1 = 0

Decimal result is: 32 + 0 + 0 + 0 + 2 + 0 = 34

(100010)₂ = (34)₁₀

Example 2: Convert (11101101)₂ to decimal.

Bits	Position	Power of 2	Value
1	2⁷ (128’s place)	2⁷ = 128	1 × 128 = 128
1	2⁶ (64’s place)	2⁶ = 64	1 × 64 = 64
1	2⁵ (32’s place)	2⁵ = 32	1 × 32 = 32
0	2⁴ (16’s place)	2⁴ = 16	0 × 16 = 0
1	2³ (8’s place)	2³ = 8	1 × 8 = 8
1	2² (4’s place)	2² = 4	1 × 4 = 4
0	2¹ (2’s place)	2¹ = 2	0 × 2 = 0
1	2⁰ (1’s place)	2⁰ = 1	1 × 1 = 1

Decimal result is: 128 + 64 + 32 + 0 + 8 + 4 + 0 + 1 = 237

(11101101)₂ = (237)₁₀

Example 3: Convert (1010111001101)₂ to decimal.

Bits	Position	Power of 2	Value
1	2¹² (4096’s place)	2¹² = 4096	1 × 4096 = 4096
0	2¹¹ (2048’s place)	2¹¹ = 2048	0 × 2048 = 0
1	2¹⁰ (1024’s place)	2¹⁰ = 1024	1 × 1024 = 1024
0	2⁹ (512’s place)	2⁹ = 512	0 × 512 = 0
1	2⁸ (256’s place)	2⁸ = 256	1 × 256 = 256
1	2⁷ (128’s place)	2⁷ = 128	1 × 128 = 128
1	2⁶ (64’s place)	2⁶ = 64	1 × 64 = 64
0	2⁵ (32’s place)	2⁵ = 32	0 × 32 = 0
0	2⁴ (16’s place)	2⁴ = 16	0 × 16 = 0
1	2³ (8’s place)	2³ = 8	1 × 8 = 8
1	2² (4’s place)	2² = 4	1 × 4 = 4
0	2¹ (2’s place)	2¹ = 2	0 × 2 = 0
1	2⁰ (1’s place)	2⁰ = 1	1 × 1 = 1

Decimal result is: 4096 + 1024 + 256 + 128 + 64 + 8 + 4 + 1 = 5581

(1010111001101)₂ = (5581)₁₀

Example 4: Convert (11010111.0111)₂ to decimal.

Integer part: (11010111)₂

Bits	Position	Power of 2	Value
1	2⁷ (128’s place)	2⁷ = 128	1 × 128 = 128
1	2⁶ (64’s place)	2⁶ = 64	1 × 64 = 64
0	2⁵ (32’s place)	2⁵ = 32	0 × 32 = 0
1	2⁴ (16’s place)	2⁴ = 16	1 × 16 = 16
0	2³ (8’s place)	2³ = 8	0 × 8 = 0
1	2² (4’s place)	2² = 4	1 × 4 = 4
1	2¹ (2’s place)	2¹ = 2	1 × 2 = 2
1	2⁰ (1’s place)	2⁰ = 1	1 × 1 = 1

Integer result = 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 215

Fractional part: (.0111)₂

Bits	Position	Power of 2	Value
0	2^-1 (1/2 place)	2^-1 = 0.5	0 × 0.5 = 0
1	2^-2 (1/4 place)	2^-2 = 0.25	1 × 0.25 = 0.25
1	2^-3 (1/8 place)	2^-3 = 0.125	1 × 0.125 = 0.125
1	2^-4 (1/16 place)	2^-4 = 0.0625	1 × 0.0625 = 0.0625

Fraction result = 0 + 0.25 + 0.125 + 0.0625 = 0.4375

Final decimal value = 215 + 0.4375 = 215.4375

(11010111.0111)₂ = (215.4375)₁₀

Example 5: Convert (1101010101.001101)₂ to decimal.

Integer part: (1101010101)₂

Bits	Position	Power of 2	Value
1	2⁹ (512’s place)	2⁹ = 512	1 × 512 = 512
1	2⁸ (256’s place)	2⁸ = 256	1 × 256 = 256
0	2⁷ (128’s place)	2⁷ = 128	0 × 128 = 0
1	2⁶ (64’s place)	2⁶ = 64	1 × 64 = 64
0	2⁵ (32’s place)	2⁵ = 32	0 × 32 = 0
1	2⁴ (16’s place)	2⁴ = 16	1 × 16 = 16
0	2³ (8’s place)	2³ = 8	0 × 8 = 0
1	2² (4’s place)	2² = 4	1 × 4 = 4
0	2¹ (2’s place)	2¹ = 2	0 × 2 = 0
1	2⁰ (1’s place)	2⁰ = 1	1 × 1 = 1

Integer result = 512 + 256 + 0 + 64 + 0 + 16 + 0 + 4 + 0 + 1 = 853

Fractional part: (.001101)₂

Bits	Position	Power of 2	Value
0	2^-1 (1/2 place)	2^-1 = 0.5	0 × 0.5 = 0
0	2^-2 (1/4 place)	2^-2 = 0.25	0 × 0.25 = 0
1	2^-3 (1/8 place)	2^-3 = 0.125	1 × 0.125 = 0.125
1	2^-4 (1/16 place)	2^-4 = 0.0625	1 × 0.0625 = 0.0625
0	2^-5 (1/32 place)	2^-5 = 0.03125	0 × 0.03125 = 0
1	2^-6 (1/64 place)	2^-6 = 0.015625	1 × 0.015625 = 0.015625

Fraction result = 0 + 0 + 0.125 + 0.0625 + 0 + 0.015625 = 0.203125

Final decimal value = 853 + 0.203125 = 853.203125

(1101010101.001101)₂ = (853.203125)₁₀

Method-2: Double Dabble Algorithm Or Shift-And-Add-3 Algorithm

In this algorithm, there are three steps involved to convert a binary number to a decimal.

Step-1: Start from the Most Significant Bit (MSB) position (left most digit). Here the total is 0 and at each step, double the previous total and add the current digit.
Step-2: Shift to the right bit position and double previous total and add the current bit value. Repeat this step till the Least Significant Bit (LSB) value is reached.
Step-3: The result at the end is the decimal equivalent value.

Example 1: Convert (101010)₂ to the decimal value.

Step-1: Start from the Most Significant Bit (MSB) position (left most digit). Here the initial total value is 0.

	MSB					LSB
Bits:	1	0	1	0	1	0

Total = 0 (Initial value is 0 for the first bit: MSB)

Least Significant Bit (LSB) = 0

Most Significant Bit (MSB) = 1

Current Bit = MSB = 1

Total_current = (Total_previous × 2) + Current Bit

Step-2:Shift to the right bit position and double previous total and add the current bit value. Repeat this until the Least Significant Bit (LSB) value is reached.

Bit Position (from MSB)	Bit Value	Total_previous	Total_current
2⁵	1	0	(0 × 2) + 1 = 1
2⁴	0	1	(1 × 2) + 0 = 2
2³	1	2	(2 × 2) + 1 = 5
2²	0	5	(5 × 2) + 0 = 10
2¹	1	10	(10 × 2) + 1 = 21
2⁰	0	21	(21 × 2) + 0 = 42

Final Decimal Value: 42

(101010)₂ = (42)₁₀

Example 2: Convert (1110110)₂ to the decimal value.

	MSB						LSB
Bits:	1	1	1	0	1	1	0

Total = 0 (Initial value for the first bit: MSB)

Least Significant Bit (LSB) = 0

Most Significant Bit (MSB) = 1

Current Bit = MSB = 1

Total_current = (Total_previous × 2) + Current Bit

Step-2: Shift to the right bit position and double previous total and add the current bit value.

Bit Position (from MSB)	Bit Value	Total_previous	Total_current
2⁶	1	0	(0 × 2) + 1 = 1
2⁵	1	1	(1 × 2) + 1 = 3
2⁴	1	3	(3 × 2) + 1 = 7
2³	0	7	(7 × 2) + 0 = 14
2²	1	14	(14 × 2) + 1 = 29
2¹	1	29	(29 × 2) + 1 = 59
2⁰	0	59	(59 × 2) + 0 = 118

Final Decimal Value: 118

(1110110)₂ = (118)₁₀

Example 3: Convert (11011011.011)₂ to the decimal value.

Step-1: Start from the Most Significant Bit (MSB) position (leftmost digit). Initial total value is 0.

MSB								LSB	Fractional Part
Bits:	1	1	0	1	1	0	1	1	.	0	1	1

Total = 0 (Initial value for the first bit: MSB)

Least Significant Bit (LSB) = 1 (for integer part)

Most Significant Bit (MSB) = 1

Current Bit = MSB = 1

Total_current = (Total_previous × 2) + Current Bit = (0 × 2) + 1 = 1

Step-2: Shift to the right bit position and double previous total and add the current bit value. Repeat until the Least Significant Bit (LSB) of the integer part is reached, then handle fractional bits by dividing by 2 for each fractional bit.

Bit Position (from MSB)	Bit Value	Total_previous	Total_current
2⁷	1	0	(0 × 2) + 1 = 1
2⁶	1	1	(1 × 2) + 1 = 3
2⁵	0	3	(3 × 2) + 0 = 6
2⁴	1	6	(6 × 2) + 1 = 13
2³	1	13	(13 × 2) + 1 = 27
2²	0	27	(27 × 2) + 0 = 54
2¹	1	54	(54 × 2) + 1 = 109
2⁰	1	109	(109 × 2) + 1 = 219
2^-1	0	219	219 + (0 × 0.5) = 219.0
2^-2	1	219.0	219 + (1 × 0.25) = 219.25
2^-3	1	219.25	219 + (1 × 0.125) = 219.375

Final Decimal Value: 219.375

(11011011.011)₂ = (219.375)₁₀

Frequently Ask Questions: Binary to Decimal Conversion

Q1: For an 8-bit binary number what is maximum unsigned and signed value in decimal?

An 8-bit unsigned binary number can have bits: b7 b6 b5 b4 b3 b2 b1 b0, where each bit is either 0 or 1. Maximum value occurs when all bits are 1 i.e. (11111111)₂.

(1 × 2⁷) + (1 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰) = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

Largest decimal for 8-bit unsigned: 255

For signed numbers, the MSB (most significant bit) is the sign bit: 0 = positive, 1 = negative.

Maximum positive value occurs when MSB = 0 and all other bits = 1 i.e. (01111111)₂

Therefore, largest signed value = (0 × 2⁷) + (1 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰) = 0 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127

Q2: How to convert 8-bit two’s complement binary number 11101011 to decimal?

In two’s complement, the most significant bit (MSB) is the sign bit:

0 shows positive value
1 shows negative value

Here, in the given number MSB = 1, so the number is negative. Take the 2's complement:

Invert Bits: (00010100)₂

Add 1: 00010100 + 1 = (00010101)₂ = (21)₁₀

Since the original number was negative (MSB = 1), we apply the negative sign: -21

Q3: Convert the 12-bit unsigned binary number 111100110101 to decimal?

(1 × 2¹¹) + (1 × 2¹⁰) + (1 × 2⁹) + (1 × 2⁸) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2²) + (1 × 2⁰) = 2048 + 1024 + 512 + 256 + 32 + 16 + 4 + 1 = (3893)₁₀

Q4: What is the largest possibe decimal value for 16-bit unsigned binary number?

For unsigned number the largest decimal is: (111111111111)₂ = (65535)₁₀

Q5: How are the fractional values represented from binary to decimal ?

In binary, the fractional part (digits after the decimal point) represents negative powers of 2:

If b is used to represents bits then (0.b₁b₂b₃....)₂ = b₁ × 2^-1 + b₂ × 2^-2 + b₃ × 2^-3 + .......

b₁ is the first bit after the point and it represents 2^-1 = 1/2¹ = 1/2 place
b₂ represents 2^-2 = 1/2² = 1/4 place
b₃ represents 2^-3 = 1/2³ = 1/8 place
And so on ...

Binary to Decimal Table

Binary	Decimal
00000001	1
00000010	2
00000011	3
00000100	4
00000101	5
00000110	6
00000111	7
00001000	8
00001001	9
00001010	10
00001011	11
00001100	12
00001101	13
00001110	14
00001111	15
00010000	16
00010001	17
00010010	18
00010011	19
00010100	20
00010101	21
00010110	22
00010111	23
00011000	24
00011001	25
00011010	26
00011011	27
00011100	28
00011101	29
00011110	30
00011111	31
00100000	32
00100001	33
00100010	34
00100011	35
00100100	36
00100101	37
00100110	38
00100111	39
00101000	40
00101001	41
00101010	42
00101011	43
00101100	44
00101101	45
00101110	46
00101111	47
00110000	48
00110001	49
00110010	50
00110011	51
00110100	52
00110101	53
00110110	54
00110111	55
00111000	56
00111001	57
00111010	58
00111011	59
00111100	60
00111101	61
00111110	62
00111111	63
01000000	64

Binary	Decimal
01000001	65
01000010	66
01000011	67
01000100	68
01000101	69
01000110	70
01000111	71
01001000	72
01001001	73
01001010	74
01001011	75
01001100	76
01001101	77
01001110	78
01001111	79
01010000	80
01010001	81
01010010	82
01010011	83
01010100	84
01010101	85
01010110	86
01010111	87
01011000	88
01011001	89
01011010	90
01011011	91
01011100	92
01011101	93
01011110	94
01011111	95
01100000	96
01100001	97
01100010	98
01100011	99
01100100	100
01100101	101
01100110	102
01100111	103
01101000	104
01101001	105
01101010	106
01101011	107
01101100	108
01101101	109
01101110	110
01101111	111
01110000	112
01110001	113
01110010	114
01110011	115
01110100	116
01110101	117
01110110	118
01110111	119
01111000	120
01111001	121
01111010	122
01111011	123
01111100	124
01111101	125
01111110	126
01111111	127
10000000	128

Binary	Decimal
10000001	129
10000010	130
10000011	131
10000100	132
10000101	133
10000110	134
10000111	135
10001000	136
10001001	137
10001010	138
10001011	139
10001100	140
10001101	141
10001110	142
10001111	143
10010000	144
10010001	145
10010010	146
10010011	147
10010100	148
10010101	149
10010110	150
10010111	151
10011000	152
10011001	153
10011010	154
10011011	155
10011100	156
10011101	157
10011110	158
10011111	159
10100000	160
10100001	161
10100010	162
10100011	163
10100100	164
10100101	165
10100110	166
10100111	167
10101000	168
10101001	169
10101010	170
10101011	171
10101100	172
10101101	173
10101110	174
10101111	175
10110000	176
10110001	177
10110010	178
10110011	179
10110100	180
10110101	181
10110110	182
10110111	183
10111000	184
10111001	185
10111010	186
10111011	187
10111100	188
10111101	189
10111110	190
10111111	191
11000000	192

Binary	Decimal
11000001	193
11000010	194
11000011	195
11000100	196
11000101	197
11000110	198
11000111	199
11001000	200
11001001	201
11001010	202
11001011	203
11001100	204
11001101	205
11001110	206
11001111	207
11010000	208
11010001	209
11010010	210
11010011	211
11010100	212
11010101	213
11010110	214
11010111	215
11011000	216
11011001	217
11011010	218
11011011	219
11011100	220
11011101	221
11011110	222
11011111	223
11100000	224
11100001	225
11100010	226
11100011	227
11100100	228
11100101	229
11100110	230
11100111	231
11101000	232
11101001	233
11101010	234
11101011	235
11101100	236
11101101	237
11101110	238
11101111	239
11110000	240
11110001	241
11110010	242
11110011	243
11110100	244
11110101	245
11110110	246
11110111	247
11111000	248
11111001	249
11111010	250
11111011	251
11111100	252
11111101	253
11111110	254
11111111	255

by Wasim Khan and it was last modified on September 14, 2025

Related Conversions

Please find the related numeric conversions.

Binary to Decimal Converter

Binary Numeral System

Example:

Decimal Numeral System

How to Convert Binary to Decimal

Method-1: Position Based Approach

How to Convert Binary Fraction to Decimal Value

Example 1: Convert (100010)₂ to decimal.

Example 2: Convert (11101101)₂ to decimal.

Example 3: Convert (1010111001101)₂ to decimal.

Example 4: Convert (11010111.0111)₂ to decimal.

Example 5: Convert (1101010101.001101)₂ to decimal.

Method-2: Double Dabble Algorithm Or Shift-And-Add-3 Algorithm

Example 1: Convert (101010)₂ to the decimal value.

Example 2: Convert (1110110)₂ to the decimal value.

Example 3: Convert (11011011.011)₂ to the decimal value.

Frequently Ask Questions: Binary to Decimal Conversion

Q1: For an 8-bit binary number what is maximum unsigned and signed value in decimal?

Q2: How to convert 8-bit two’s complement binary number 11101011 to decimal?

Q3: Convert the 12-bit unsigned binary number 111100110101 to decimal?

Q4: What is the largest possibe decimal value for 16-bit unsigned binary number?

Q5: How are the fractional values represented from binary to decimal ?

Binary to Decimal Table

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Binary to Decimal Converter

Binary Numeral System

Example:

Decimal Numeral System

How to Convert Binary to Decimal

Method-1: Position Based Approach

How to Convert Binary Fraction to Decimal Value

Example 1: Convert (100010)2 to decimal.

Example 2: Convert (11101101)2 to decimal.

Example 3: Convert (1010111001101)2 to decimal.

Example 4: Convert (11010111.0111)2 to decimal.

Example 5: Convert (1101010101.001101)2 to decimal.

Method-2: Double Dabble Algorithm Or Shift-And-Add-3 Algorithm

Example 1: Convert (101010)2 to the decimal value.

Example 2: Convert (1110110)2 to the decimal value.

Example 3: Convert (11011011.011)2 to the decimal value.

Frequently Ask Questions: Binary to Decimal Conversion

Q1: For an 8-bit binary number what is maximum unsigned and signed value in decimal?

Q2: How to convert 8-bit two’s complement binary number 11101011 to decimal?

Q3: Convert the 12-bit unsigned binary number 111100110101 to decimal?

Q4: What is the largest possibe decimal value for 16-bit unsigned binary number?

Q5: How are the fractional values represented from binary to decimal ?

Binary to Decimal Table

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Example 1: Convert (100010)₂ to decimal.

Example 2: Convert (11101101)₂ to decimal.

Example 3: Convert (1010111001101)₂ to decimal.

Example 4: Convert (11010111.0111)₂ to decimal.

Example 5: Convert (1101010101.001101)₂ to decimal.

Example 1: Convert (101010)₂ to the decimal value.

Example 2: Convert (1110110)₂ to the decimal value.

Example 3: Convert (11011011.011)₂ to the decimal value.