数字电路教学课件：chapter1-1

1、Number systems Number system use positional notation to represent value. The position of the character (numeral) in a character string (collection of possible numerals) indicate value as well as the character itself. is the number of numeral characters in the character set of a positional number sys

2、tem. is a constant that represents the value of a position. Different position has different weight. It is the integer power of radix. Radix = r; Weight = rn; Character set = 0, 1, , r-1 Represent number N of radix r Positional Notation Polynomial Notation Radix=10 ; Character set : 0,1,2,3,4,5,6,7,

3、8,9 Weight=10n ; Ex. The decimal number 536 is (536)10 Binary number Radix=2 ; Character set :0,1 Weight=2n ; Ex. The binary number 0110 is (0110)2 Radix=8 ; Character set : 0,1,2,3,4,5,6,7 Weight=8n ; Ex. The decimal number 536 is (536)8 Hexadecimal number Radix=16 ; Character set : 0,1,2,3,4,5,6,7

4、,8,9,A,B,C,D,E,F Weight=16n ; Ex. (1AD.B)16=1 162+A 161+D 160+B 16-1 1. Partition the binary number into groups of four, starting at the radix point and going left and right. 2. Each group of four corresponds to a single hexadecimal digit. 1. Partition the binary number into groups of three, startin

5、g at the radix point and going left and right. 2. Each group of three corresponds to a single octal digit. Each hexadecimal digit corresponds to four binary digits. Each octal digit corresponds to three binary digits Polynomial Notation Evaluate each term in the Polynominal Polynomial Notation Evalu

6、ate each term in the Polynomial Integral part Polynomial Notation1.Convert the integer by successive divisionN= integer to be convertedr= radix of new numberQ= quotient of divide operationR=remainder of divide operationR=MSD in radix rN/r=QR save R as LSDInput N and rQ/r=QR save RQ=0 Output radix r

7、numberNoYes fractional part Polynomial Notation2.Convert the fraction by successive multiplicationNf= fraction to be convertr= radix of new numberP= product, where IpFp and means tied together Fp=fractional part of PIp=integer part of PYes Ip =LSD Output radix r numberr*Nf=Ip Fp, Ip=MSD Input Nf and

8、 rFp =0r*Fp=Ip Fp, save IpNo e.g., (63)e.g., (63)1010=( ? )=( ? )2 26321=b01=b53153171=b11=b21=b31=b42222remainderremainderwith inaccuracy less than 2 2-10-10 0.7060.7062=1.4122=1.4121 1 b b1 10.4120.4122=0.8242=0.8240 0 b b2 20.8240.8242=1.6482=1.6481 1 b b3 30.6480.6482=1.2962=1.2961 1 b b4 40.2960.2962=0.5922=0.5920 0 b b5 50.5920.5922=1.1842=1.1841 1 b b6 6 0.1840.1842=0.3682=0.3680 0 b b7 7 0.3680.3682=0.7362=0.7360 0 b b8 8 0.7360.7362=1.2=1.4724721 1 b b9 9 because because 0.4720.4720.50.5，round off(round off(“四舍五入四舍五入