Decimal to Binary, Octal, Hexadecimal, and Other Base n numbers
Decimal to Binary, Octal, Hexadecimal, and Other Base n numbers
1.1 Decimal to Binary
(45)₁₀ to ( )₂
1st Method LCM
45/2 Quotient = 22 , Remainder = 1
22/2 Quotient = 11, Remainder = 0
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
Take From Last Quotient to Upper Last Remainder
1 0 1 1 0 1
(45)₁₀ = (101101)₂
1.2 Decimal to Octal
(45)₁₀ to ( )₈
2 Methods
- Decimal to Octal
- Decimal to Binary — Binary to Octal
Decimal to Octal
(45)₁₀ to ( )₈
1st Method LCM
45/8 Quotient = 5, Remainder = 5
5/8 Quotient = 5 , Remainder = 0
5 5
(45)₁₀ to (55 )₈
2nd Method
Decimal to Binary — Binary to Octal
(46)₁₀ to ( )₂
46/2 Quotient = 23 , Remainder = 0
23/2 Quotient = 11, Remainder = 1
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
1 0 1 1 1 0
(46)₁₀ = (101110)₂
Binary to Octal
1 0 1 1 1 0
Divide the Number in 2 Parts
101 and 110
1 0 1
²²x1+²¹x0+²⁰x1
4x1+ 2x0 + 1x1
4+1 = 5 (1st Digit) — — — — — — 1
110
²²x1 + ²¹x1 + ²⁰x0
4x1 + 2x1+1x0
4+2 = 6 (2nd Digit) — — — — — — 2
= 56
(101110)₂ = (56)₈
1.3 Decimal to Hexadecimal
(47)₁₀ to ( )₁₆
2 Methods
- Decimal to Hexadecimal
- Decimal to Binary — Binary to Hexadecimal
1st Method LCM
(47)₁₀ to ( )₁₆
47/16 Quotient = 32, Remainder = 15
32/16 Quotient = 2, Remainder = 0
Where in Hexadecimal F = 15
So There is 2 and F
(47)₁₀ to (2F )₁₆
2nd Method Decimal to Binary — Binary to Hexadecimal
(47)₁₀ to ( )₂
47/2 Quotient = 23 , Remainder = 1
23/2 Quotient = 11, Remainder = 1
11/2 Quotient = 5 , Remainder = 1
5/2 Quotient = 2, Remainder = 1
2/2 Quotient = 1, Remainder = 0
1 0 1 1 1 1
(47)₁₀ to (101111 )₂
Binary to Hexadecimal
1 0 1 1 1 1
Where 1 0 in binary is 2
and 1111 is F
(101111 )₂ = (2F )₁₆
1.4 Decimal to N Base Number
(47)₁₀ to ( )₆
1st Method LCM
47/6 Quotient = 7, Remainder = 5
7/6 Quotient = 1 , Remainder = 1
(47)₁₀= (115)₆
