Numeral Systems Calculator With Steps

Convert the number 12₁₀ to base-2, by successively dividing by 2, until the quotient is zero. The result will be the number formed from the remainders written from right to left.

12	:	2	=	6	remainder: 0
6	:	2	=	3	remainder: 0
3	:	2	=	1	remainder: 1
1	:	2	=	0	remainder: 1

12₁₀ = 1100₂

Convert whole number part 12 of the number 12.3₁₀ to base-2, by successively dividing by 2, until the quotient is zero. The result will be the number formed from the remainders written from right to left.

12	:	2	=	6	remainder: 0
6	:	2	=	3	remainder: 0
3	:	2	=	1	remainder: 1
1	:	2	=	0	remainder: 1

12₁₀ = 1100₂

Let's convert the decimal part 0.3 of the number 12.3₁₀ to base-2, using successively multiplying by 2, until the decimal part of the product turns out to be zero or the required number of digits after the decimal point is reached. If after multiplying the whole number part is not zero, then you need to replace the value of the whole number part with zero. The result will be a number of integer parts of product written from left to right.

0.3	·	2	=	0.6
0.6	·	2	=	1.2
0.2	·	2	=	0.4
0.4	·	2	=	0.8
0.8	·	2	=	1.6
0.6	·	2	=	1.2
0.2	·	2	=	0.4
0.4	·	2	=	0.8
0.8	·	2	=	1.6

0.3₁₀ = 0.010011001₂
12.3₁₀ = 1100.010011001₂

Let's convert the number 10011₂ to base-10 by first writing down the position of each digit in the number from right to left, starting at zero.

Position	4	3	2	1	0
Number	1	0	0	1	1

Each digit position will be a power of 2, because the number system is base-2. It is necessary to write down the sum, each term in which will be the product of each digit of the number 10011₂ and 2 to the power, which is determined by the position in the number.

10011₂ = 1 ⋅ 2⁴ + 0 ⋅ 2³ + 0 ⋅ 2² + 1 ⋅ 2¹ + 1 ⋅ 2⁰ = 19₁₀

Let's convert the number 11.101₂ to base-10 by first writing down the position of each digit in the number

Position	1	0	-1	-2	-3
Number	1	1	1	0	1

Each digit position will be a power of 2, because the number system is base-2. It is necessary to write down the sum, each term in which will be the product of each digit of the number 11.101₂ and 2 to the power, which is determined by the position in the number.

11.101₂ = 1 ⋅ 2¹ + 1 ⋅ 2⁰ + 1 ⋅ 2^-1 + 0 ⋅ 2^-2 + 1 ⋅ 2^-3 = 3.625₁₀

Convert the number 1583₁₀ to base-16, by successively dividing by 16, until the quotient is zero. The result will be the number formed from the remainders written from right to left.

1583	:	16	=	98	remainder: 15,   15 = F
98	:	16	=	6	remainder: 2
6	:	16	=	0	remainder: 6

1583₁₀ = 62F₁₆

Convert whole number part 1583 of the number 1583.56₁₀ to base-16, by successively dividing by 16, until the quotient is zero. The result will be the number formed from the remainders written from right to left.

1583	:	16	=	98	remainder: 15,   15 = F
98	:	16	=	6	remainder: 2
6	:	16	=	0	remainder: 6

1583₁₀ = 62F₁₆

Let's convert the decimal part 0.56 of the number 1583.56₁₀ to base-16, using successively multiplying by 16, until the decimal part of the product turns out to be zero or the required number of digits after the decimal point is reached. If after multiplying the whole number part is not zero, then you need to replace the value of the whole number part with zero. The result will be a number of integer parts of product written from left to right.

0.56	·	16	=	8.96
0.96	·	16	=	15.36,   15 = F
0.36	·	16	=	5.76
0.76	·	16	=	12.16,   12 = C
0.16	·	16	=	2.56
0.56	·	16	=	8.96
0.96	·	16	=	15.36,   15 = F
0.36	·	16	=	5.76
0.76	·	16	=	12.16,   12 = C
0.16	·	16	=	2.56

0.56₁₀ = 0.8F5C28F5C2₁₆
1583.56₁₀ = 62F.8F5C28F5C2₁₆= 62F.(8F5C2)₁₆

Let's convert the number A12DCF₁₆ to base-10 by first writing down the position of each digit in the number from right to left, starting at zero.

Position	5	4	3	2	1	0
Number	A	1	2	D	C	F

Each digit position will be a power of 16, because the number system is base-16. It is necessary to write down the sum, each term in which will be the product of each digit of the number A12DCF₁₆ and 16 to the power, which is determined by the position in the number.
A₁₆ = 10₁₀
D₁₆ = 13₁₀
C₁₆ = 12₁₀
F₁₆ = 15₁₀

A12DCF₁₆ = 10 ⋅ 16⁵ + 1 ⋅ 16⁴ + 2 ⋅ 16³ + 13 ⋅ 16² + 12 ⋅ 16¹ + 15 ⋅ 16⁰ = 10563023₁₀

Let's convert the number A12DCF.12A₁₆ to base-10 by first writing down the position of each digit in the number

Position	5	4	3	2	1	0	-1	-2	-3
Number	A	1	2	D	C	F	1	2	A

Each digit position will be a power of 16, because the number system is base-16. It is necessary to write down the sum, each term in which will be the product of each digit of the number A12DCF.12A₁₆ and 16 to the power, which is determined by the position in the number.
A₁₆ = 10₁₀
D₁₆ = 13₁₀
C₁₆ = 12₁₀
F₁₆ = 15₁₀

A12DCF.12A₁₆ = 10 ⋅ 16⁵ + 1 ⋅ 16⁴ + 2 ⋅ 16³ + 13 ⋅ 16² + 12 ⋅ 16¹ + 15 ⋅ 16⁰ + 1 ⋅ 16^-1 + 2 ⋅ 16^-2 + 10 ⋅ 16^-3 = 10563023.07275390625₁₀

Let's convert the number 1010100011₂ to base-10 by first writing down the position of each digit in the number from right to left, starting at zero.

Position	9	8	7	6	5	4	3	2	1	0
Number	1	0	1	0	1	0	0	0	1	1

Each digit position will be a power of 2, because the number system is base-2. It is necessary to write down the sum, each term in which will be the product of each digit of the number 1010100011₂ and 2 to the power, which is determined by the position in the number.

1010100011₂ = 1 ⋅ 2⁹ + 0 ⋅ 2⁸ + 1 ⋅ 2⁷ + 0 ⋅ 2⁶ + 1 ⋅ 2⁵ + 0 ⋅ 2⁴ + 0 ⋅ 2³ + 0 ⋅ 2² + 1 ⋅ 2¹ + 1 ⋅ 2⁰ = 675₁₀

Convert the number 675₁₀ to base-16, by successively dividing by 16, until the quotient is zero. The result will be the number formed from the remainders written from right to left.

675	:	16	=	42	remainder: 3
42	:	16	=	2	remainder: 10,   10 = A
2	:	16	=	0	remainder: 2

675₁₀ = 2A3₁₆
1010100011₂ = 2A3₁₆