CSI_Chapter2:Binary Values and Number Systems

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2.1 Numbers and Computing

Number A unit of an abstract mathematical system subject to the laws of arithmetic (succession, addition, multiplication) .

2.2 Positional Notation

Positional notation 位置计数法 A system of expressiong numbers in which the digits are arranged in succesion, the position of each digit has a place values, and the number is equal to the sum of the products of each digit by its place value.

Bianry, Octal and Hexadecimal二进制，八进制和十六进制

The base-2 (binary) number system is particularly important in computing.

Arithmetic in Different Bases

Power-of-2 Number Systems

Converting from Base 10 to Other Bases

WHILE (the quotient is not zero)
  Divide the decimal number by the new base
  Make the remainder the next digit to the left in the answer
  Replace the decimal number with the quotient

Binary Values and Computing

Each storage location within a computer contains either a low-voltage signal, equated with a 0, or a high-voltage signal, equated with a 1. Note that a storage location cannot be empty: It must contain either a 0 or a 1.

Each stotage unit is called a binary digit, or bit 比特 for short.

• 1 byte字节 = 8 bits

Word A group of one or more bytes; the number of bits in a word is the word length of the computer

For example, IBM 370 architecture had half words (2 bytes), full words (4 bytes) and double words (8 bytes).

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