数电数字逻辑2

1、Chapter 2: Number systems and codes Positional number system : representation and conversion Representations of negative binary numbersBCD codes and Gray code2.1 Positional number systemsUse few digit to express infinite values Each digit position has a different weightDefinition:Number digit base/r

2、adixPositional number systemsNumber: a string of digits;Each digit position has a different weight;Radix is written as 10 in any system.Decimal system: base is 10, the digit may be 0 to 9Binary system: base is 2, the digit may be 0 or 1bit: one digit in binary system; Examples of positional number s

3、ystemBinary numbers with certain width ;The numbers always be set as 0.xxxxxxxx;We can take these numbers as integers !Example for an 8-bit binary number: Positional number system in digital designMSB/LSB binary to decimal: based on definitions;Examples :Conversion: from one system to another binary

4、 to decimal Examples :Conversion: from one system to another Conversion: from Decimal to binary For integer numbers : divided by 2, get its remainders;Examples for 8-bit binary numbers:17989 442211521 1 1 0 0 1 1 0 1Conversion: from Decimal to binary For decimal fraction numbers : multiplied by radi

5、x, and get its integers; Examples for 8-bit binary numbers:0.170.34 0.681.360.721.440.881.761.52Different number systemsP.28 Table 2-1Numbers and word widthNumber is written as a word (string of digit); An n-bit word may have 2n different forms;When word width n increase: For integer, number range i

6、s increase; For fraction, number resolving power is increase.A short way to represent numbers Binary to octal: 3-bit to 1 digit;Binary to hexadecimal: 4-bit to 1 digit;Key point: divide from the radix point !Examples :Conversion: from one system to another Summary: p.31 Table 2-2Operations for unsigned numbersBasic rules: 0+0=0 1+0=1 1+1=10 10-1=1 Addition and subtractionC:carry S:sum B:borrow D:difference Operations for unsigned numbersBasic rules: