C Language---Binary

1. What is a binary

Rounding mechanism, every few into one. The number of values in a position is a few steps in the operation.

In-Life: Decimal, 12 binary (12 months is 1 years), six decimal (60 seconds is 1 minutes)

In computer programming: binary, octal, 16 decimal, Binary

2. The role of the binary

Use a finite number to represent all values.

In decimal, for example, use 0~9 numbers to represent all values.

For example:

(1) Value 9: Use the number 9 to indicate

(2) Value 10: Use numbers 1 and 0 to denote

3, the rules of the system

(1) n binary uses numbers between 0~n-1 to represent all values

1) Binary 0 1

2) octal 0 1 2 3 4 5 6 7

3) Decimal 0 1 2 3 4 5 6 7 8 9

4) Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F (a~f i.e. 10~15)

(2) n the value of the binary, each in the calculation is every n into a

1) in decimal when a value of 10 o'clock is indicated, the rule of decimal is required on the 9+1, and therefore 10 is used to represent the value 10

2) binary when a value of 2 o'clock is required, the binary rule is every binary one, so use 10 to represent the value 2

4. Binary conversion

(1) Concept

1) cardinality n is the cardinality of N, for example: the base of the decimal is 10

2) bit to the value of each bit of the description, right-to-left is the lowest bit, the highest bit, the lowest bit using 0, in order to increase the high direction

For example: a bit of 123 3 is the bit of 0,2 is the bit of 2

3) The right to n is N, for example: the right of the decimal is 10

4) the unit value corresponding to each position n^ (i-1)

(2) Decimal turn n binary

To even remove the rewind remainder

(3) n binary to Decimal

Sum by bit

5. Differentiate into system

(1) Decimal: No modification

(2) Octal: value before plus 0,0111

(3) 16 binary: value before plus 0x,0x111

(4) Binary: value before plus 0b,0b111

6. Knowledge of the system

(1) Decimal: For developers, binary: The computer can recognize the language, that is, 0, 1 encoding

(2) 1 x 16 binary bits = 4 bits hex: 0~f binary: 0000~1111 16 binary exists, more useful for the convenience of binary representation

Practice

Exercise 1. Calculates the value of decimal 42 converted to binary, octal, hexadecimal, respectively.

Decimal: 42;

Binary: 42/2=21 more than 0;

21/2=10 more than 1;

10/2=5 more than 0;

5/2=2 more than 1;

2/2=1 more than 0;

1/2=0 more than 1;

101010

Octal: 42/8=5 more than 2;

5/8=0 more than 5;

52

Hex: 42/16=2 more than 10;

2/16=0 more than 2;

2 A

Exercise 2. (*) calculates the decimal value corresponding to the binary 11010110.

Binary: 11010110;

Decimal: 0*2^0+1*2^1+1*2^2+0*2^3+1*2^4+0*2^5+1*2^6+1*2^7=214

Exercise 3. (*) calculates the decimal value corresponding to the octal 075.

Octal: 075;

Decimal: 5*8^0+7*8^1=61

Exercise 4. (*) calculates the decimal value corresponding to the hexadecimal 0xa8.

Hex: 0xa8;

Decimal: 8*16^0+10*16^1=168

C Language---Binary