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2’s Complement 4-Bit Saturator

2’s Complement 4-Bit Saturator. Lecture L4.6. Equality Detector. XNOR. X Y Z 0 0 1 0 1 0 1 0 0 1 1 1. X. Z. Y. Z = !(X $ Y). Z = 1 if A=B=C. 4 x 1. MUX. s1. s0. Y. 0 0 C0 0 1 C1 1 0 C2 1 1 C3. Multiplexers. C0. C1. Y. C2. C3. s1. s0.

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2’s Complement 4-Bit Saturator

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  1. 2’s Complement 4-Bit Saturator Lecture L4.6

  2. Equality Detector XNOR X Y Z 0 0 1 0 1 0 1 0 0 1 1 1 X Z Y Z = !(X $ Y)

  3. Z = 1 if A=B=C

  4. 4 x 1 MUX s1 s0 Y 0 0 C0 0 1 C1 1 0 C2 1 1 C3 Multiplexers C0 C1 Y C2 C3 s1 s0

  5. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 A multiplexer is a digital switch 0 0

  6. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 0 1

  7. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 1 0

  8. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 1 1

  9. A 2 x 1 MUX Z = A & !s0 # B & s0

  10. S Y 0 A 1 B ProblemHow would you make aQuad 2-to-1 MUX? Quad 2-to-1 MUX [A3..A0] [Y3..Y0] [B3..B0] S

  11. X = 011101 Y = 0111 X = 110101 Y = 1000 NASA Tech Briefs November 2001 A Y0 Y1 Y2 Y3 B X0 X1 X2 X3 X4 X5 c0 X = 111111 Y = 1111 X = 000101 Y = 0101 c1

  12. ABEL // Title: 2s-complement 4-bit Saturator // Author: R. E. Haskell // Ref: NASA Tech Briefs, Nov. 2001 // Description: 4-bit output Y = // -8 if 6-bit input X is <= -8 // +7 if 6-bit input X is >= +7 // X otherwise MODULE sat64 INTERFACE ([X5..X0] -> [Y3..Y0]); TITLE '2s complement 4-bit saturator' // Author: R. E. Haskell

  13. DECLARATIONS " Input Pins " X5..X0 PIN ISTYPE 'com'; X = [X5..X0]; " 6-bit input " Output Pins " Y3..Y0 PIN ISTYPE 'com'; Y = [Y3..Y0]; " 4-bit output "Definitions A = [X5,!X5,!X5,!X5]; B = [X3,X2,X1,X0]; c0 = !(X3 $ X4); c1 = !(X4 $ X5); s = c0 & c1; EQUATIONS Y = !s & A # s & B; END A Y0 Y1 Y2 Y3 X0 X1 X2 B X3 X4 X5 c0 c1

  14. Top-level Design

  15. // Title: Absolute value function // Author: R. E. Haskell // Input: Y = 4-bit signed number (-8 to +7) // Output: Z = magnitude of input number (0 to 8) MODULE absval interface([Y3..Y0] -> [Z3..Z0]); DECLARATIONS " INPUT PINS " Y3..Y0 PIN; Y = [Y3..Y0]; " 4-bit input " OUTPUT PINS " Z3..Z0 PIN ISTYPE 'com'; Z = [Z3..Z0]; " 4-bit output

  16. DECLARATIONS " INPUT PINS " Y3..Y0 PIN; Y = [Y3..Y0]; " 4-bit input " OUTPUT PINS " Z3..Z0 PIN ISTYPE 'com'; Z = [Z3..Z0]; " 4-bit output EQUATIONS when (Y == 0) then Z = ^b0000; when (Y == 1) then Z = ^b0001; when (Y == 2) then Z = ^b0010; when (Y == 3) then Z = ^b0011; when (Y == 4) then Z = ^b0100; when (Y == 5) then Z = ^b0101; when (Y == 6) then Z = ^b0110; when (Y == 7) then Z = ^b0111; when (Y == 8) then Z = ^b1000; when (Y == 9) then Z = ^b0111; when (Y == ^h0A) then Z = ^b0110; when (Y == ^h0B) then Z = ^b0101; when (Y == ^h0C) then Z = ^b0100; when (Y == ^h0D) then Z = ^b0011; when (Y == ^h0E) then Z = ^b0010; when (Y == ^h0F) then Z = ^b0001; END absval

  17. Top-level Design

  18. // Title : 2's Complement 4-Bit Saturator // Author : R. E. Haskell // Description : 7-segment displays show the signed output // of the 2's complement 4-bit saturator MODULE sat4bit DECLARATIONS sat64 INTERFACE ([X5..X0] -> [Y3..Y0]); sat FUNCTIONAL_BLOCK sat64; absval INTERFACE ([Y3..Y0] -> [Z3..Z0]); abs FUNCTIONAL_BLOCK absval; hex7seg INTERFACE ([D3..D0] -> [a,b,c,d,e,f,g]); d7R FUNCTIONAL_BLOCK hex7seg;

  19. " INPUT PINS " SW5..SW0 PIN 6,5,4,3,2,1; " S6, Switches 3,4; S7, Switches 1-4 SW = [SW5..SW0]; " OUTPUT PINS " LEDR3..LEDR0 PIN 40,41,43,44 ISTYPE 'com'; " LEDs 13-16 LEDR = [LEDR3..LEDR0]; [a,b,c,d,e,f,g] PIN 15,18,23,21,19,14,17 ISTYPE 'com'; Rsegments = [a,b,c,d,e,f,g]; " Rightmost 7-segment digit minus PIN 66 ISTYPE 'com'; " segment g of left 7seg display EQUATIONS sat.[X5..X0] = SW; LEDR = sat.[Y3..Y0]; abs.[Y3..Y0] = sat.[Y3..Y0]; d7R.[D3..D0] = abs.[Z3..Z0]; Rsegments = d7R.[a,b,c,d,e,f,g]; minus = sat.Y3; END

  20. Verilog // Title: 2s-complement 4-bit Saturator // Author: R. E. Haskell // Ref: NASA Tech Briefs, Nov. 2001 // Description: 4-bit output Y = // -8 if 6-bit input X is <= -8 // +7 if 6-bit input X is >= +7 // X otherwise module sat64(X,Y); input [5:0] X; output [3:0] Y;

  21. module sat64(X,Y); input [5:0] X; output [3:0] Y; wire [3:0] Y; wire c0, c1, s; wire [3:0] A; wire [3:0] B; assign A[3] = X[5]; assign A[2:0] = {~X[5],~X[5],~X[5]}; assign B = {X[3],X[2],X[1],X[0]}; assign c1 = X[3] ~^ X[4]; assign c0 = X[4] ~^ X[5]; assign s = c0 & c1; assign Y = {4{~s}} & A | {4{s}} & B; endmodule A Y0 Y1 Y2 Y3 X0 X1 X2 B X3 X4 X5 c0 c1

  22. Top-level Design

  23. // Title: Absolute value function // Author: R. E. Haskell // Input: Y = 4-bit signed number (-8 to +7) // Output: Z = magnitude of input number (0 to 8) module absval(Y,Z); input [3:0] Y; output [3:0] Z; reg [3:0] Z;

  24. module absval(Y,Z); input [3:0] Y; output [3:0] Z; reg [3:0] Z; always @(Y) case(Y) 0: Z = 4'b0000; 1: Z = 4'b0001; 2: Z = 4'b0010; 3: Z = 4'b0011; 4: Z = 4'b0100; 5: Z = 4'b0101; 6: Z = 4'b0110; 7: Z = 4'b0111; 8: Z = 4'b1000; 9: Z = 4'b0111; 'hA: Z = 4'b0110; 'hb: Z = 4'b0101; 'hC: Z = 4'b0100; 'hd: Z = 4'b0011; 'hE: Z = 4'b0010; 'hF: Z = 4'b0001; default: Z = 4'b0000; // 0 endcase endmodule

  25. Top-level Design

  26. // Title : 2's Complement 4-Bit Saturator // Author : R. E. Haskell // Description : 7-segment displays show the signed output // of the 2's complement 4-bit saturator module sat4bit(SW,LEDR,LEDG,AtoG,gg); input [5:0] SW; output [3:0] LEDR; output [5:0]LEDG; output [6:0] AtoG; output gg;

  27. module sat4bit(SW,LEDR,LEDG,AtoG,gg); input [5:0] SW; output [3:0] LEDR; output [5:0]LEDG; output [6:0] AtoG; output gg; wire [6:0] AtoG; wire [3:0] LEDR; wire [5:0] LEDG; wire gg; wire [3:0] Y; wire [3:0] Z; assign LEDR = Y; assign LEDG = SW; assign gg = Y[3]; sat64 sat(.X(SW),.Y(Y)); hex7seg d7R(.D(Z),.AtoG(AtoG)); absval abs(.Y(Y),.Z(Z)); endmodule

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