# סיכום כל החומר במערכות ספרתיות

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For more please visit www.nsof.info r 10 :1 0 15(23.1) 25 35 15 13.2niii ma r== = + + = 10 r :10 88(242.1875) (?)242 / 8 30 (2) 0.18758 1.5 (1)30 / 8 3(6) 0.158 4.0 (4) (362.14)3/ 8 0 (3) 08 0LSBMSB= = = == =

t r :1 . t - r . 2,4,8,16 3,9,27 :8 22(2501.24) (?)(010 101 000 001. 010 100) " 3 : 32 8 =.2 . 10 . BCD ) 8421 :(10(171.7) (0001 0111 0001. 0111)BCD= : = .10 642 3642 3(3) (?)16 0 4 0 2 1( 3) 3 (1001)== + + + = 1 . Excess-3 : 3 , .10 3(1955) 4 12 8 8 (0100110010001000)Excess= = : N - 9 N " .10 310 3(3) 3 3 (0110)(9 3) 6 3 (1001)ExcessExcessN= + = + = : BCD .

: = 9 .

) Hamming :( 2 .100 001 - = 2 . . K , K-1 , [ ] ( 1) / 2 k . Gray : , ) = 1 .( Gray ) :(1 . , .2 . ) .(3 . - .4 . - . Gray ) :(1 . , .2 . XOR .3 . - .

:Even Parity 1 .Odd Parity 0 - .10110 10111 OddParity Even Parity

Fixed Point : _ _ . _ _ ) .(

Floating Point :Enumber Mr = 53.491r= 10 10 . : 5.3491 . E 01 .15.349110 53.491EMr = = Sign / Magnitude : .0 = . r-1 = .10 10 10 10( 5) (0/ 05) ; ( 5) (9 / 05) + = = 2 - 0 . . ' ' ' :12 1n - r-1 :10 10 10 1010 2 10 2( 631) (0 / 631) ; ( 631) (9 / 368)( 11) (0 / 1011) ; ( 11) (1/ 0100)+ = =+ = = 2 - 0 . ' ' ' :12 1n : - LSB .14 10001 11000112 10011 11001126 11001001100101

- r :10 10 1010 2 2( 631) (9 / 368 1) (9 / 369)( 11) (111/ 0100 1) (111/ 0101) = + = = + = - - 1 - LSB ) ' , - "- " - "+" .(- : , 2 ) - 1 .(

: .1 . 0 . :X +0 = X; X +1= 1 ; X + X = X; X +YZ =(X +Y)(X +Z)X X = X; X X' = 0 ; X + X' = 1 (X +Y)(X +Y') = X; X(X +Y) = X(X +Y)+Z = X +(Y +Z) XY' +Y = X +Y(XY)Z = X(YZ) = XYZ XY +YZ + X'Z = XY + X'ZX(Y +Z) = XY + XZ (X +Y)(X' +Z) = XZ + X'YXY + XY' = X ; X + XY = X (X +Y)(Y +Z)(X' +Z) =(X +Y)(X' +Z) - : ( ...) ( ' ' ') ' ( ) ' ' ' ' X Y Z XY Z XYZ X Y Z + + + = = + + :101.111011.1101101001111010101101000 :1 . - Xor .2 . .3 . .

' :- " . .- . , " 1 " - "0 " , "+" - "- " , .Xor / Xnor :( ) '' ... ( ...) '' ' ... (( ...) ') '0 , 1 'x y x y x yx y z x y zx y z x y zx y z x y zx x x x = = = = = = =

x y z ( ) ' x y z 1 1 1 11 1 1 1

XOR 1 - .XNOR 1 .

:::: ': ( ) ': ( ) ': ' ': ' 'AND xyOR x yNOT xNAND xyNOR x yXOR x y xy x yXNOR xy x y x y+++ = + = ) ( . , :{ } { } { } ; ' ( ) ' ; ' ( ) ' ; ; ' NOR x y NAND xy = + = + = = + - - NOT - AND )NAND ( NOT - OR )NOR ( . " - - .

Minterm & Maxterm :Max Min Z Y XX+Y+ZXYZ0000 X+Y+ZXYZ1001 ... :SOP " 1 ." :POS " 0 ." :( , , ) (3, 4, 5) (0, 7) (0,1, 2, 6, 7) (0, 7)' (0,1, 2, 6, 7) (0, 7)d ddf x yzf= + = += + : POS )D =LSB :(CDCDCDCD 10110100 231000AB 675401AB 1415131211AB10119810AB - ) (...( ) ( ' ') f D B D B = + + = . ) ( = . : 2 . 3 . ) dont care :( " : X , d , . . / :- ) A - 'A ( , .- ) A B ( 2 / .

- AND - OR - NAND1 . - SOP .2 . Fan In ) ' .(3 . " AND - OR ) AND-OR-AND-OR... .(4 . .5 . NAND .6 . - NOT ) .( : NOT ) " - ( " NAND .

Full Adder :' ' ' ' ' '( )out in in inS A B CABC ABC ABC ABCC AB AC BC AB A B C= == + + += + + = +

Look Ahead Carry Generator : - Carry " .1 i i i i i i i i i i i i iS A B C P C G A B C G P C+= = = = + :2 1 1 1 1 1 0 0 0( ) C G PC G PG PC = + = + + - 2 ) r ( " FA :1 . r-1 " .2 . r-1 .3 . r .4 . 3 , " ' ) 1 .(5 . " 1 .6 . 4 .7 . r-1 .8 . 6 .9 . - FA .10 . CorrectionUnit - FA 9 - Carry - FA 1 - FA 10 r .

, MUX - : Decoder - : Encoder - : - :MUX 4x1 1 . 0 . - 4 x 2 . 1 . Priority Encoder 1 , - 1 , Dont Care . 0 . - 4x2 .

: E )Enable ( 0 0 .

Comperator ) :(

- - G :

1 . A3>B3 .3 3 ' A B 2 . A3=B3, A2>B2 .3 3 2 2 ' A B A B 3 . A3=B3, A2=B2, A1>B1 .3 3 2 2 1 1 ' A B A B AB 4 . A3=B3, A2=B2, A1=B1, A0>B0 .3 3 2 2 1 1 0 0 ' A B A B A B A B ) 1-4 :( OR .

Static Hazard , , . .Hazard 1 : 1 - 0 ) SOP .(Hazard 0 : 0 - 1 ) POS .(

Quine Mclluskey1 . / .2 . : # 1 # 1 # 100- -0,1,2,3 0000-00-00,1 0,2 0000000 00-1001-1,3 2,3 10001 0010 1 2 1 001132 : , ) ( . " 0 1 ) " .(3 . :14 13 12 11 6 5 4 1 X X X X 4,6,12,14X X 12,13X X 1,5

Shift Register with Parallel Load :

/ :' a / s : 1 , 0 .2-bit FAA BCin CoutS+4 bit ComperatorL AB A3 A2 A1 A0B3 B2 B1 B0+ ++XY FAX Ya / s S B outB in 000110110123E00011011EX Y00011011E For more please visit www.nsof.info....2 1 0m :Rom Read Only Memory 2nm ROM n - .2n- .m - ) OR .( :PLA Programmable Login Array PLA 3x4x2 :1' ' ' ' ' ' ' 2 ' ' ' ' F ab ac bc F bc ac abc = + + = + + PLA :F2F1cba 1100-bc 110-0ac 1-00ab 1-111abc - PLA : :PLA Programmable Login Array :SR-Latch : S=R=1 - S=R=0 / . S,R - SR-Latch S=R=1 .Gated SR-Latch : Q(t+1)RSG Q001 0101 1011 -111 D-latch / Transparent Latch : Q(t+1)G Q0 D1 Edge Triggered D Flip-Flop : - D " " " .- - 0 - 1 .- - 1 - 0 .- " " .- NOT - Master . , - Slave -Master . FF :- TPC-Q : . ) ( .- TCC-Q : , . TPC-Q > TCC-Q - TS (Setup Time) . D TS .- TH (Hold Time) . D TH . :- TS - TH .- TS - TH .- " : TCC-Q > TH . ) Finite State Machine :(1 . . " .2 . n : 2 :nn m) .(3 . , .4 . .5 . : . Moore : . . Mealy : . . Moore Mealy .6 . : FSM , . , . .Flip Flops : ) .( ) .(Y(t)=RY(t-1)+S :SR-FF SR SRY(t)RSRSY(t)Y(t-1) Y(t-1)00d000 0100110 1011001 -110d11 Y(t)=JY(t-1)+KY(t-1) :JK-FF JK JKY(t) K J K J Y(t) Y(t-1)Y(t-1)00d000 010d110 1011d01 Y(t-1)110d11 D-FF : Y(t+1)=D D DY(t) D D Y(t) Y(t-1)0 0 0 0 01 1 1 1 00 0 11 1 1T-FF : Y(t)=TY(t-1) T TY(t) T T Y(t) Y(t-1)Y(t-1)0 0 0 0Y(t-1)1 1 1 01 0 10 1 1 FF FF : : JK SR . " FF )SR ( - FF (JK) : " S - R R S Y(t) y(t-1) K Jd0 0 0 0 00d 1 1 0 0d0 0 0 1 0 ... ) ( 1 . ) ( " -FF .2 . " - FF .3 . ) .(4 . :NS PSX=1X=0 ZY2Y1ZY2Y1 y2y1 10001000 00101110 00001001 00111111 PS ) Present State .(NS ) Next State .(X .Z - PS .5 . : ) .(NS PSZX=1ZX=0 1A0BA 0C0DB 0A0BC 0C1DD 6 . : 7 . " . ) ( 1 . .2 . .3 . .4 . .5 . FF ) ' " .(NS PSX=1X=0 ZK2 J2 K1 J1 ZK2 J2 K1 J1y2y1 1d0d00d1d000 01dd100dd110 0d01d0d11d01 01d0d10d0d11 6 . - FF Z .7 . . : : " " , . / Ripple Counter : : 256 " 2 Clear . 2 , 128 :128 256 / 2 =.- - T-FF Clear .-Clear 0 - T-FF .- - T-FF ! " 6-bit Ripple Counter - clk 2 7-bit Ripple Counter ) - 0 127 - 0 .(Qi - Qi-1 : :2 A, B ) Distinguishable ( ) ( A, B . n n-1 .K :2 A, B K K :2 A,B A B . , A - B " .K :A - B K " K . Moore : : ( A B C DF G ) ( E ) x=0 x=1 ECBGED CAGADG ( A F ) ( B C D G ) ( E ) . . . :- - X=0 - X=1 ) ABCDFG ( ) E .(- ) 0= x - DE CBG E .(- .- .- , . :NSPS X=1X=0 00A = 00F = 00BD = 00CG = 01E = / : / " , . 2 / . / : .NSNS X=1X=0 PS X=1X=0 PS 0C0B=A00 0E1D=B00 0C0E=C00 0E0B=D00 0A0C=E01 : A,B A B .: 2nnDecoder2n012X/Z0/0BCD0/00/11/00/0 1/01/01/1A S Q R Q S G R S Q R Q G D D Q clk Q DQ G Q DQ G Q Data clk=MasterSlave . . AND.F1F2ab ac bc abc abcORS R Q Q = S Q R QclkQ0 Q1 T0 clk Q0 Clear " 1 " T1 Q1 T2 Q2 T3 Q3 T4 Q4 T5 Q5