1024₁₀ → binary, hex and octal — number base conversion

edge caseone value in four bases at once

Answer

10000000000₂ = 400₁₆ = 2000₈

Why this example is worth doing

A power of two shown in every base the tool supports, which makes the structural point that all four representations are the same number and only the notation differs. Powers of two are exactly the values that are a single 1 followed by zeros in binary, and the position of that 1 is the exponent. The page uses this to introduce the kilobyte ambiguity — 1024 against 1000 — which is a real source of confusion in storage specifications.

Try your own input in the Binary ⇄ decimal ⇄ hex ⇄ octal. Convert between any two bases, integers and fractions, with the positional working.

How the answer is reached

Base 10 to base 2

Convert 1024 from base 10 to base 2. The sign is carried across unchanged; only the magnitude is converted.

Positional expansion of the input — Base 10 to base 2
digit	value	weight	weight (base 10)	digit x weight
1	1	10^3	1000	1000
0	0	10^2	100	0
2	2	10^1	10	20
4	4	10^0	1	4
			total	1024

Integer part: divide by 2 and read the remainders bottom to top.

Read the last column bottom to top. ↑ — Base 10 to base 2
n	divide by	quotient	remainder
1024	1024 ÷ 2	512	0
512	512 ÷ 2	256	0
256	256 ÷ 2	128	0
128	128 ÷ 2	64	0
64	64 ÷ 2	32	0
32	32 ÷ 2	16	0
16	16 ÷ 2	8	0
8	8 ÷ 2	4	0
4	4 ÷ 2	2	0
2	2 ÷ 2	1	0
1	1 ÷ 2	0	1

1024 (base 10)10000000000 (base 2)

Base 10 to base 16

Convert 1024 from base 10 to base 16. The sign is carried across unchanged; only the magnitude is converted.

Positional expansion of the input — Base 10 to base 16
digit	value	weight	weight (base 10)	digit x weight
1	1	10^3	1000	1000
0	0	10^2	100	0
2	2	10^1	10	20
4	4	10^0	1	4
			total	1024

Integer part: divide by 16 and read the remainders bottom to top.

Read the last column bottom to top. ↑ — Base 10 to base 16
n	divide by	quotient	remainder
1024	1024 ÷ 16	64	0
64	64 ÷ 16	4	0
4	4 ÷ 16	0	4

1024 (base 10)400 (base 16)

Base 10 to base 8

Convert 1024 from base 10 to base 8. The sign is carried across unchanged; only the magnitude is converted.

Positional expansion of the input — Base 10 to base 8
digit	value	weight	weight (base 10)	digit x weight
1	1	10^3	1000	1000
0	0	10^2	100	0
2	2	10^1	10	20
4	4	10^0	1	4
			total	1024

Integer part: divide by 8 and read the remainders bottom to top.

Read the last column bottom to top. ↑ — Base 10 to base 8
n	divide by	quotient	remainder
1024	1024 ÷ 8	128	0
128	128 ÷ 8	16	0
16	16 ÷ 8	2	0
2	2 ÷ 8	0	2

1024 (base 10)2000 (base 8)