Decimal, binary, octal, hexadecimal conversions

The decimal number consists of a total of 10 numeric characters in 0~9, 10 in each of the decimal digits, and a maximum number of 9 in each decimal digit.

The binary number consists of 0 and 12 numeric characters, and in binary one, the maximum number is 1 for each bit in the binary.

Octal is composed of a total of 8 numeric characters in the 0~7, "every eight into one" in octal, and the maximum number is 7 in each bit in octal.

Hexadecimal is composed of 0~9, A, B, C, D, E, f a total of 16 characters, in hexadecimal "every 16 in one", in hexadecimal the largest number is F.

First of all, talk about decimal to binary binary:

Example: decimal to go binary

Take 55 divided by 2.

55/2=27 Yu 1, take 27 divided by 2,27/2=13 1, take 13 divided by 2,13/2=6 1, take 6 divided by 2,6/2=3 the remaining 0, take 3 divided by 2,3/2=1 to 1,

Then the decimal 55 is converted to binary is 110111

Decimal Turn octal

Example: decimal 534 turn octal

Take 534 divided by 8,534/8=66 6, 66 divided by 8 equals 8 + 2, 8 divided by 8 equals 1 + 0, then decimal 534 turns octal is 1026.

Decimal Turn hex

Example: decimal 300 turn hex

Take 300 divided by 16 equals 18 + 12 (12 in the 16 binary in C, 10 is a, B is 11, until F is 15), take 18 divided by 16 equals 1 more than 2, take 1 divided by 16, equals 0, do not represent, then decimal 300 is converted to 16 in the result of 12C.

Binary conversion to Decimal

Example: 111=1*4+1*2+1*1=7;

It has a comparison table:

1	1	1	1	1	1	1	1
128	64	32	16	8	4	2	1

See how many bits are in the binary, and then add them apart.

Binary conversion to octal

There is a way to put the number of binary from right to left, three bit a group, not enough to fill 0

Column: 111=4+2+1=7

11001 split into 001 and 011,001=1,011=2+1=3;

Then the 11001 conversion to octal is 31.

Binary conversion to hexadecimal

Reference binary to octal, but it is from right to left, four bit a group, not enough to fill 0

1101101: Split into 1101, 0110

Two binary values are computed separately, 1101=8+4+0+1=13, 13 in hex is D

0110=4+2=6 , then the binary 1101101 conversion to 16 binary is 6D.

octal into binary

From back to front, each digit is converted to three-bit binary by decimal, and the vacancy is 0

7=4+2+1=111:77, split apart

So the octal 77 conversion bit binary is 111111.

Octal into decimal

Sub-clause: 555=5*8 's 2-time Square +5*8 +5=320+40+5=365;

octal conversion bit hex

First, the octal conversion bit 2 is binary, then the binary conversion bit hexadecimal

For example: Octal 721 first converted to binary, take apart

7=111 , 2=010,1=001,

Get 277 binary 111010001, then convert to 16, from right to left, four a group, not enough to fill 0

111010001 to 0001,1101,0001

0001=1 , 1101=8+4+1=13, hexadecimal words, for d,0001=1, then convert to 16 binary is 1D1

16 Binary conversion to binary

Convert each digit to binary, each number four bits, less than four bits, front 0

2=0010,F=15=1111,D=13=1101:2FD, split apart, separate

Then convert to binary to get 1011111101

16 Binary conversion to octal

First convert 16 into binary, (principle a hexadecimal to four bit binary), in the binary conversion into octal, (the principle is from right to left three, not enough to fill 0)

The following: hexadecimal 2FD conversion binary 1011111101, in the binary 1011111101 into octal, from the right to the left, four a split, not enough to fill 0

1011111101 split into 001,011,111,101, calculated separately

001=1 , 011=2+1=3,111=4+2+1=7,101=4+1=5, then the last conversion to octal will get 1375.

16 Binary conversion to decimal

Convert to decimal similar to octal binary

2D=2*16: A +13=2*16+13=45 of the first party

Hexadecimal 2D converted to decimal get decimal 45

Decimal, binary, octal, hexadecimal conversions