First chapter Conversion

Numbering conversion

Decimal: There are 10 cardinality: 0,1,2,3,4,5,6,7,8,9

Binary: There are 2 cardinality: 0,1

Octal: There are 8 cardinality: 0,1,2,3,4,5,6,7

Hex: There are 16 cardinality: 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f (a=10,b=11,c=12,d=13,e=14,f=15)

Conversion between decimal and other binary

One, (1) decimal- binary: decimal number divided by 2, except until 0 o'clock the remainder is written in the opposite direction, that is, the binary number.

Cases:

The resulting binary is: 11101 (2) [quotient is even when the remainder is 0; odd time remainder is 1]

(2) binary --Decimal

Calculation formula: AX20+BX21+CX22+...+MX2 (n-1) =

A represents the first digit to the right of the binary, and B represents the second digit to the right of the binary ... m represents the number of digits to the right of the binary (n-1).

Example: 1011001

1x20+0x21+1x22+1x23+0x24+0x25+1x26

=1+8+16+64

=89

Number of binary right digits	1	2	3	4	5	6	7	8
decimal number	1	2	4	8		32	64	128
Formula prototypes	20	21st	22	23	24	25	26	27

Second, (1) decimal--Eight decimal number is divided into 8, until the quotient is 0, the remainder is written in reverse order, that is, the octal system.

Example: 139 write eight binary as 213 (8)

(2) octal--Decimal

Calculation formula: ax80+bx81+cx82+...+mx8 (n-1) =

Principle with Binary

From the right nth bit	8	7	6	5	4	3	2	1
8 (n-1)			83		style= "font-size:16px;" >  bayi
Actual number under decimal	2097152	262144	32768	4096	512	64	8	1

Three, (1) decimal--16 binary

Principle with Binary

(2) hexadecimal--Decimal

Principle with Binary

163	162	161	160
4096	256	16	1

Conversions between other binaries

Binary conversion to octal : for integers, use right-to-left each three-bit group, not enough three bits to the left of 0, each group is converted separately (right to left), that is, eight decimal.

Cases:

Octal is converted to binary: replaces each octet by a three-bit binary number. (Not enough three-bit front-fill 0)

Example: (1 7 3 5)

001 111 011 101

So, (1111011101) for the resulting binary number

Binary conversion to hex : Because 2 of the 4-square = 16, the same as the two-to-eight method, the binary number of each four bits are represented by a hexadecimal numeral, the integer part of the decimal point to the right to the left of each four-bit group conversion,

The number of decimal points starts from the left-to-right for each four-bit group.

Example: (1001 0111 0111 1001)

9 7 7 9

16 binary to binary: The conversion can be done as long as each hexadecimal number is represented by a four-bit corresponding binary number.

Example: (8 7 6 5)

1000 0111 0110 0101

Therefore, (1000 0111 0110 0101) for the resulting binary number

First chapter Conversion