# Binary to Decimal - Decimal to Binary

## Convert binary to decimal (bin to dec) or decimal to binary (dec to bin)

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Binary to Decimal Converter

You can input in any of the fields and get equivalent values.
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## How to Convert Binary to Decimal?

• For binary to decimal (whether it is 8 bit, 16 bit or 32 bit) , we can use positional Notation method. Multiply each binary digit with its place value and then add the product values

• Eg to Convert (10011011)2 8 bit binary to decimal

• Start at 20, evaluating it as "1". Increment the exponent by one for each power. We have to write for 8 elements,128, 64, 32, 16, 8, 4, 2, 1

• Multiply binary digit with power values.(1*128)+(0*64)+(0*32)+(1*16)+(1*8)+(0*4)+(1*2)+(1*0)

• = 128+0+0+16+8+0+2+1 Total the Values which is 155

• (10011011)2 = (155)10

• For 16 bit binary to decimal, you can do it the same way, with the various positions representing values from 20=1 to 216=65,536

• For 32 bit binary to decimal, the position represent values from 20=1 to 231=2,147,483,648

## How To Convert Decimal / Numeric to Binary?

• Decimal to Binary converter - Divide the number repeatedly by 16 till quotient is zero.

• To convert 16 decimal to binary , Divide the number 16 by 2,the quotient is 8 ,remainder is 0

• Again, Divide the number 8 by 2,the quotient is 4 ,remainder is 0

• Divide the number 4 by 2,the quotient is 2 ,remainder is 0

• Divide the number 2 by 2,the quotient is 1 ,remainder is 0

• Divide the number 1 by 2,the quotient is 0 ,remainder is 1

• Write the remainder from top to botton 10000

• (16)10 = (10000)2

## Decimal to Binary Converter table

DecimalBinary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
16 10000
17 10001
18 10010
19 10011
20 10100
24 11000
48 110000
50 110010
64 1000000
75 1001011
100 1100100
128 10000000
255 11111111
512 1000000000
1024 10000000000
2048 100000000000
512 8 bit
1024 16 bit
2048 32 bit

Binary Decimal
10 2
100 4
0101 5
0110 6
1000 8
1010 10
1011 11
1100 12
1101 13
1111 15
10000 16
10010 18
10101 21
11001 25
11111 31
100000 32
1000000 64
10000000 128
100000000 256

## FAQ on Binary to Decimal Converter Calculator

• Binary is number system having two values as 0 and 1.
Digits(0 and 1) in this system is called bit.
Used to represent two possible states ON/Off as 0 and 1

• Decimal is a numbering system which having 10 as base.
Each digit is denoted by integers from 0 to 9.
Also called as Hindu-Arabic Number system /Arabic Number system

• For Negative,we have to write binary representation of decimal number.
For eg -25 ,first write binary for 25=00011001.
Then,flip the 0 and 1 00011001 as 11100110.
Finally add 1 to this ,11100111.
This is the Final output.
(-25)10=(11100111)2

• converting decimals to signed binary numbers.
For Eg:-12
There is a negative, so the first digit will be a one.
Divide the 12 by 2 we get quotient is 6, remainder 0.
Again divide 6 by 2, we get quotient is 3, remainder 0
divide 3 by 2 , we get quotient is 1, remainder 1
divide 1 by 2 quotientis 0, remainder 1,we have to write the remainder from top to bottom.
This gives four digits, but there are seven digits needed. So, place zeros in the extra places.
The first digit is 1 because it is a negative number.
Next three digits are all 0 because there are four and seven are needed.
The last four digits go from bottom to top: 1100
-12 = 10001100

• Multiply the fractional decimal number by 2.
Then the integral part of resultant decimal number will be first digit of fraction binary number.
Repeat the process using only fractional part of decimal number .