.CT Holden Rohrer .CT Applications of Engineering: Pd 3 .CT Phrase Project ================================================================================ .CT Table of Contents 1 . . . . . . . . . . . . . . . . . . . . .Problem Statement 2 . . . . . . . . . . . . . . . . . . . . . . .Truth Table 3 . . . . . . . . . . . . . . . .Unsimplified Boolean Expressions 4 . . . . . . . . . . . . . . . . . Karnaugh-like depthy mapping 5 . . . . . . . . . . . . . . . . Simplified Boolean Expressions 6 . . . . . . . . . . . . . . . . . . . . . . Logic Diagram 7 . . . . . . . . . . . . . . . . . . . . . . Difficulties 8 . . . . . . . . . . . . . . . . .Appendix A: AutoCAD Schematic 9 . . . . . . . . . . . . . . . . Appendix B: Complete Breadboard ================================================================================ .CT Problem Statement The objective of this project is to, using 74LS series chips (00, 04, 08, 11, 21, 32) and an anode seven-segment display (FND507) deisplay a 16-letter phrase with varying input switches. Jumper wires, a breadboard, and a "Breadboard Assistant" will be used to connect these components.t The phrase I will display is "AUTOCADSCHEMATIC," each letter displayed corresponding directly to the following cube vertices/switch positions (so chosen that any two consecutive states only require one switch instead of four like in 0111->1000): 0000 -> 0001 -> 0011 -> 0010 -> 0110 -> 0111 -> 0101 -> 0100 -> 1100 -> 1101 -> 1111 -> 1110 -> 1010 -> 1011 -> 1001 -> 1000. The breadboard will use the following wire colors convention: - GND = BROWN - PWR = WHITE - W = BROWN - !W = WHITE - X = BLACK - !X = YELLOW - Y = GREEN - !Y = RED - Z = GRAY - !Z = BLUE - AND = ORANGE - OR = PURPLE - NOT = RED The Seven-Segment Display will use the following light naming convention: _______ | a | | |b |f | |_______| | g | |e |c | | |_______| d ================================================================================ .CT Truth Table W X Y Z | VAL | A B C D E F G (1=OFF, 0=ON) ========+=====+============== 0 0 0 0 | A | 0 0 0 1 0 0 0 0 0 0 1 | U | 1 0 0 0 0 0 1 0 0 1 1 | T | 1 1 1 0 0 0 0 0 0 1 0 | O | 0 0 0 0 0 0 1 0 1 1 0 | C | 0 1 1 0 0 0 1 0 1 1 1 | A | 0 0 0 1 0 0 0 0 1 0 1 | D | 1 0 0 0 0 1 0 0 1 0 0 | S | 0 1 0 0 1 0 0 1 1 0 0 | C | 0 1 1 0 0 0 0 1 1 0 1 | H | 1 1 0 1 0 0 0 1 1 1 1 | E | 0 1 1 0 0 0 0 1 1 1 0 | M | 0 1 0 1 0 1 1 1 0 1 0 | A | 0 0 0 1 0 0 0 1 0 1 1 | T | 1 1 1 0 0 0 0 1 0 0 1 | I | 1 1 1 1 0 0 1 1 0 0 0 | C | 0 1 1 0 0 0 0 ================================================================================ .CT Unsimplified Boolean Expressions ___ __ _ _ _ _ __ A = WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ __ _ _ _ __ __ _ _ _ __ ___ B = WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ __ _ _ __ _ __ ___ C = WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ ____ _ _ _ _ _ __ D = WXYZ + WXYZ + WXYZ + WXYZ + WXYZ + WXYZ _ __ E = WXYZ _ _ _ F = WXYZ + WXYZ ___ __ _ _ _ _ __ G = WXYZ + WXYZ + WXYZ + WXYZ + WXYZ ================================================================================ .CT Berkeley's ABC! .CT --------------- I used Berkeley's ABC: github.com/berkeley-abc/abc. .CT Genlib File GATE inv 2.3 O=!a; PIN * INV 1 999 0.9 0.3 0.9 0.3 GATE nand 3.5 O=!(a*b); PIN * INV 1 999 0.9 0.3 0.9 0.3 GATE and2 3.5 O=a*b; PIN * NONINV 1 999 0.9 0.3 0.9 0.3 GATE and3 4.7 O=a*b*c; PIN * NONINV 1 999 0.9 0.3 0.9 0.3 GATE and4 7 O=a*b*c*d; PIN * NONINV 1 999 0.9 0.3 0.9 0.3 GATE or 3.5 O=a+b; PIN * NONINV 1 999 0.9 0.3 0.9 0.3 GATE buf 1 O=a; PIN * NONINV 1 999 0.9 0.3 0.9 0.3 GATE zero 0 O=CONST0; GATE one 0 O=CONST1; .CT PLA file .i 4 .o 7 .ilb w x y z .ob a b c d e f g 0000 0001000 0001 1000001 0011 1110000 0010 0000001 0110 0110001 0111 0001000 0101 1000010 0100 0100100 1100 0110000 1101 1101000 1111 0110000 1110 0101011 1010 0001000 1011 1110000 1001 1111001 1000 0110000 .e On a Bourne shell with abc binary built in current dir: $ ./abc -c "read circ.pla; read_library gathing.genlib; strash;\ collapse; strash; rewrite; strash; dc2; map; choice; map; print_gates;\ write struct.eqn;" $ sed -e 's/new_n//g' -e 's/_//g' struct.eqn > struct.eqn.tmp $ mv struct.eqn{.tmp,} #with some custom cleanup (NAND, moving !x...) .CT Network Structure from Berkeley's ABC a = NAND(y,x) * z; 16 = !w * !y; 17 = x * !w; 18 = 17 + 16; 20 = !z * y; 21 = 20 + 18; 23 = z + !x; b = NAND(23,21); 25 = !16; 26 = z + !y; 27 = 26 + 17; 28 = y * w; 29 = NAND(z,x); 30 = 29 + 28; c = 25 * 30 * 27; 32 = z * !y; 33 = 32 + 20; 34 = 33 * w; 35 = !z + y; 36 = 18 * 35 * 23; d = 36 + 34; 38 = !z * x; e = 38 * 16; 40 = 28 * 38; 41 = 32 * 17; f = 41 + 40; 43 = !x * w; 44 = 43 + 26; 45 = 35 + x; g = NAND(45,44); Total cost: - 12 2AND = 3 74LS08 - 4 NAND = 1 74LS00 - 5 NOT = 1 74LS04 - 2 3AND = 1 74LS11 - 12 OR = 3 74LS32