Day-15: Number Conversion.

Decimal to Binary Conversion.

Decimal to binary calculation steps, Let’s calculate a decimal value 12345 to the binary numbers.

Divide by the base 2 to get the digits from the remainders:

Division by 2	Quotient	The remainder (Digit)	Bit #
(123456)/2	61728	0	0
(61728)/2	30864	0	1
(30864)/2	15432	0	2
(15432)/2	7716	0	3
(7716)/2	3858	0	4
(3858)/2	1929	0	5
(1929)/2	964	1	6
(964)/2	482	0	7
(482)/2	241	0	8
(241)/2	120	1	9
(120)/2	60	0	10
(60)/2	30	0	11
(30)/2	15	0	12
(15)/2	7	1	13
(7)/2	3	1	14
(3)/2	1	1	15
(1)/2	0	1	16

= (11110001001000000)₂

Decimal to Octal Conversion.

Decimal to octal calculation steps, Let’s calculate a decimal value 9875421 to the binary numbers.

Divide by the base 8 to get the digits from the remainders:

Division by 8	Quotient	The remainder (Digit)	Digit #
(9875421)/8	1234427	5	0
(1234427)/8	154303	3	1
(154303)/8	19287	7	2
(19287)/8	2410	7	3
(2410)/8	301	2	4
(301)/8	37	5	5
(37)/8	4	5	6
(4)/8	0	4	7

= (45527735)₈

Decimal to Hexadecimal Conversion.

Decimal to hex calculation steps, Let’s calculate a decimal value 7891011 to the binary numbers.

Divide by the base 16 to get the digits from the remainders:

Division by 16	Quotient	The remainder (Digit)	Digit #
(7891011)/16	493188	3	0
(493188)/16	30824	4	1
(30824)/16	1926	8	2
(1926)/16	120	6	3
(120)/16	7	8	4
(7)/16	0	7	5

= (786843)₁₆

Octal to Decimal Conversion.

Octal to decimal calculation steps, Let’s calculate a decimal value of 1234567 to the binary numbers.

1234567 = (1 × 8⁶) + (2 × 8⁵) + (3 × 8⁴) + (4 × 8³) + (5 × 8²) + (6 × 8¹) + (7 × 8⁰) = 342391

Octal to Binary Conversion.

Convert each octal digit to 3 binary digits (see conversion table below):
165421
= 1 6 5 4 2 1
= 001 110 101 100 010 001
= 001110101100010001

Octal to Hexa Decimal Conversion.

Convert every octal digit to 3 binary digits, then convert every 4 binary digits to1 hex digit (see conversion tables):
652341
= 6 5 2 3 4 1
= 110 101 010 011 100 001
= 11 0101 0100 1110 0001
= 3 5 4 E 1
= 354E1

Binary to Decimal Conversion.

Let’s calculate a binary value of 101011101 to the Decimal numbers.

(101011101)₂ = (1 × 2⁸) + (0 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = (349)₁₀

Binary to Octal Conversion.

Let’s calculate a binary value of 110110111 to the Octal numbers.

Convert every 3 binary digits (from bit0) to octal digit (see conversion table below):
110110111
= 110 110 111
= 6 6 7
= 667

Binary to Hexa Decimal Conversion.

Let’s calculate a binary value of 11011001 to the Hexa Decimal numbers.

Convert every 4 binary digits (from bit0) to a hex digit (see conversion table below):
11011001
= 1101 1001
= D 9
= D9

Hexa Decimal to Decimal Conversion.

Decimal calculation steps

Let’s calculate a Hexa Decimal value of dabc9856b to the Decimal numbers.

(DABC9856B)₁₆ = (13 × 16⁸) + (10 × 16⁷) + (11 × 16⁶) + (12 × 16⁵) + (9 × 16⁴) + (8 × 16³) + (5 × 16²) + (6 × 16¹) + (11 × 16⁰) = (58716685675)₁₀

Hexa Decimal to Octal Conversion.

Let’s calculate a Hexa Decimal value of bdacf7d3a to the Octal numbers.

Convert each hex digit to 4 binary digits and then convert each 3 binary digits to octal digits (see conversion tables below):
bdacf7d3a
= b d a c f 7 d 3 a
= 1011 1101 1010 1100 1111 0111 1101 0011 1010
= 101 111 011 010 110 011 110 111 110 100 111 010
= 5 7 3 2 6 3 6 7 6 4 7 2
= 573263676472

Hexa Decimal to Binary Conversion.