1101 1010₂ → hex and octal — number base conversion

coregrouping by 4 and by 3 bits

Answer

DA₁₆ = 332₈

Why this example is worth doing

The shortcut that makes hex worth knowing: because sixteen is two to the fourth, each hex digit is exactly four bits and conversion is pure grouping with no arithmetic at all. Octal groups by three for the same reason. The page shows the grouping from the right-hand end and warns about the one real pitfall — padding the leftmost group with leading zeros rather than trailing ones, which silently multiplies the value.

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 2 to base 16

Convert 11011010 from base 2 to base 16. The sign is carried across unchanged; only the magnitude is converted.

Positional expansion of the input — Base 2 to base 16
digit	value	weight	weight (base 10)	digit x weight
1	1	2^7	128	128
1	1	2^6	64	64
0	0	2^5	32	0
1	1	2^4	16	16
1	1	2^3	8	8
0	0	2^2	4	0
1	1	2^1	2	2
0	0	2^0	1	0
			total	218

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

Read the last column bottom to top. ↑ — Base 2 to base 16
n	divide by	quotient	remainder
218	218 ÷ 16	13	A
13	13 ÷ 16	0	D

Shortcut: group the binary digits in 4s outward from the radix point — Base 2 to base 16
side	groups of 4	base 16
integer side (pad left)	1101 1010	DA

11011010 (base 2)DA (base 16)

Base 2 to base 8

Convert 11011010 from base 2 to base 8. The sign is carried across unchanged; only the magnitude is converted.

Positional expansion of the input — Base 2 to base 8
digit	value	weight	weight (base 10)	digit x weight
1	1	2^7	128	128
1	1	2^6	64	64
0	0	2^5	32	0
1	1	2^4	16	16
1	1	2^3	8	8
0	0	2^2	4	0
1	1	2^1	2	2
0	0	2^0	1	0
			total	218

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

Read the last column bottom to top. ↑ — Base 2 to base 8
n	divide by	quotient	remainder
218	218 ÷ 8	27	2
27	27 ÷ 8	3	3
3	3 ÷ 8	0	3

Shortcut: group the binary digits in 3s outward from the radix point — Base 2 to base 8
side	groups of 3	base 8
integer side (pad left)	011 011 010	332

11011010 (base 2)332 (base 8)