Computer Organization and Design Fundamental 書籍作者： David Tarnoff 投影片製作者：陳鍾誠 第 2 章 Numbering Systems

2.1 Unsigned Binary Counting

位數增長

固定位數

2.2 Binary Terminology Least Significant Bit or LSBMost Significant Bit or MSB

2.3 Unsigned Binary to Decimal Conversion

2 進位轉 10 進位

表示法的最大數字 8 位元無號數的最大數字 256 無法表示為 8 位元無號數 n 位元無號數能表示的最大數字

2.4 Decimal to Unsigned Binary Conversion 將 133 轉為 2 進位 =

10 進位轉 2 進位的流程

2.5 Binary Representation of Analog Values

聲波的類比訊號

類比 – 數位轉換公式

2.6 Sampling Theory

不同取樣位數的結果

Both of these examples are situations where aliasing has occurred. If a signal's frequency is faster than the sampling rate, then information will be lost, and the collected data will never be able to duplicate the original.

取樣過慢的結果

Nyquist Theorem To avoid aliasing, the rate at which samples are taken must be more than twice as fast as the highest frequency you wish to capture. This is called the Nyquist Theorem For example, the sampling rate for audio CDs is 44,100 samples/second. Dividing this number in half gives us the highest frequency that an audio CD can play back, i.e., 22,050 Hz.

取樣率的範例 For an analog telephone signal, a single sample is converted to an 8-bit integer. If these samples are transmitted across a single channel of a T1 line which has a data rate of 56 Kbps (kilobits per second), then we can determine the sampling rate. This means that the highest analog frequency that can be transmitted across a telephone line using a single channel of a T1 link is 7,000÷2 =3,500 Hz. That's why the quality of voices sent over the telephone is poor when compared to CD quality.

2.7 Hexadecimal Representation

2.8 Binary Coded Decimal

2.9 Gray Codes

Table 2-3 Derivation of the Four-Bit Gray Code