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1 66 robfinch 
`timescale 1ns / 1ps
2 
// ============================================================================
3 
//        __
4 
//   \\__/ o\    (C) 2012-2022  Robert Finch, Waterloo
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//    \  __ /    All rights reserved.
6 
//     \/_//     robfinch@finitron.ca
7 
//       ||
8 
//
9 
//      BCDMath.sv
10 
//
11 
// BSD 3-Clause License
12 
// Redistribution and use in source and binary forms, with or without
13 
// modification, are permitted provided that the following conditions are met:
14 
//
15 
// 1. Redistributions of source code must retain the above copyright notice, this
16 
//    list of conditions and the following disclaimer.
17 
//
18 
// 2. Redistributions in binary form must reproduce the above copyright notice,
19 
//    this list of conditions and the following disclaimer in the documentation
20 
//    and/or other materials provided with the distribution.
21 
//
22 
// 3. Neither the name of the copyright holder nor the names of its
23 
//    contributors may be used to endorse or promote products derived from
24 
//    this software without specific prior written permission.
25 
//
26 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
27 
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
28 
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
29 
// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
30 
// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
31 
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
32 
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
33 
// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
34 
// OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
35 
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36 
//
37 
// ============================================================================
38 
//
39 
// Could use the following approach for add/sub but it ends up being larger
40 
// than using an adjustment lookup table.
41 
 
42 
module BCDAddNyb(ci,a,b,o,c);
43 
input ci;               // carry input
44 
input [3:0] a;
45 
input [3:0] b;
46 
output [3:0] o;
47 
output c;
48 
 
49 
wire c0;
50 
 
51 
reg [4:0] hsN0;
52 
always  @*
53 
begin
54 
        hsN0 = a[3:0] + b[3:0] + ci;
55 
        if (hsN0 > 5'd9)
56 
                hsN0 = hsN0 + 3'd6;
57 
end
58 
assign o = hsN0[3:0];
59 
assign c = hsN0[4];
60 
 
61 
endmodule
62 
 
63 
module BCDAdd(ci,a,b,o,c);
64 
input ci;               // carry input
65 
input [7:0] a;
66 
input [7:0] b;
67 
output [7:0] o;
68 
output c;
69 
 
70 
wire c0,c1;
71 
 
72 
wire [4:0] hsN0 = a[3:0] + b[3:0] + ci;
73 
wire [4:0] hsN1 = a[7:4] + b[7:4] + c0;
74 
 
75 
BCDAddAdjust u1 (hsN0,o[3:0],c0);
76 
BCDAddAdjust u2 (hsN1,o[7:4],c);
77 
 
78 
endmodule
79 
 
80 
module BCDAdd4(ci,a,b,o,c,c8);
81 
input ci;               // carry input
82 
input [15:0] a;
83 
input [15:0] b;
84 
output [15:0] o;
85 
output c;
86 
output c8;
87 
 
88 
wire c0,c1,c2;
89 
assign c8 = c1;
90 
 
91 
wire [4:0] hsN0 = a[3:0] + b[3:0] + ci;
92 
wire [4:0] hsN1 = a[7:4] + b[7:4] + c0;
93 
wire [4:0] hsN2 = a[11:8] + b[11:8] + c1;
94 
wire [4:0] hsN3 = a[15:12] + b[15:12] + c2;
95 
 
96 
BCDAddAdjust u1 (hsN0,o[3:0],c0);
97 
BCDAddAdjust u2 (hsN1,o[7:4],c1);
98 
BCDAddAdjust u3 (hsN2,o[11:8],c2);
99 
BCDAddAdjust u4 (hsN3,o[15:12],c);
100 
 
101 
endmodule
102 
 
103 
module BCDAddN(ci,a,b,o,co);
104 
parameter N=24;
105 
input ci;               // carry input
106 
input [N*4-1:0] a;
107 
input [N*4-1:0] b;
108 
output [N*4-1:0] o;
109 
output co;
110 
 
111 
genvar g;
112 
generate begin : gBCDAddN
113 
reg [4:0] hsN [0:N-1];
114 
wire [N:0] c;
115 
 
116 
assign c[0] = ci;
117 
assign co = c[N];
118 
 
119 
for (g = 0; g < N; g = g + 1)
120 
        always @*
121 
                hsN[g] = a[g*4+3:g*4] + b[g*4+3:g*4] + c[g];
122 
 
123 
for (g = 0; g < N; g = g + 1)
124 
        BCDAddAdjust u1 (hsN[g],o[g*4+3:g*4],c[g+1]);
125 
end
126 
endgenerate
127 
 
128 
endmodule
129 
/*
130 
module BCDAdd8NClk(clk, a, b, o, ci, co);
131 
parameter N=33;
132 
input clk;
133 
input [N*8-1:0] a;
134 
input [N*8-1:0] b;
135 
output [N*8-1:0] o;
136 
input ci;
137 
output co;
138 
 
139 
reg [N:0] c;
140 
wire [N:0] d;
141 
assign c[0] = ci;
142 
assign co = c[N];
143 
 
144 
genvar g;
145 
generate begin : gBCDadd
146 
for (g = 0; g < N; g = g + 1) begin
147 
        BCDAdd u1 (c[g],a[g*8+7:g*8],b[g*8+7:g*8],o[g*8+7:g*8],d[g+1]);
148 
 
149 
        always_ff @(posedge clk)
150 
                c[g+1] <= d[g+1];
151 
end
152 
end
153 
endgenerate
154 
endmodule
155 
*/
156 
 
157 
module BCDSub(ci,a,b,o,c);
158 
input ci;               // carry input
159 
input [7:0] a;
160 
input [7:0] b;
161 
output [7:0] o;
162 
output c;
163 
 
164 
wire c0,c1;
165 
 
166 
wire [4:0] hdN0 = a[3:0] - b[3:0] - ci;
167 
wire [4:0] hdN1 = a[7:4] - b[7:4] - c0;
168 
 
169 
BCDSubAdjust u1 (hdN0,o[3:0],c0);
170 
BCDSubAdjust u2 (hdN1,o[7:4],c);
171 
 
172 
endmodule
173 
 
174 
module BCDSub4(ci,a,b,o,c,c8);
175 
input ci;               // carry input
176 
input [15:0] a;
177 
input [15:0] b;
178 
output [15:0] o;
179 
output c;
180 
output c8;
181 
 
182 
wire c0,c1,c2;
183 
assign c8 = c1;
184 
 
185 
wire [4:0] hdN0 = a[3:0] - b[3:0] - ci;
186 
wire [4:0] hdN1 = a[7:4] - b[7:4] - c0;
187 
wire [4:0] hdN2 = a[11:8] - b[11:8] - c1;
188 
wire [4:0] hdN3 = a[15:12] - b[15:12] - c2;
189 
 
190 
BCDSubAdjust u1 (hdN0,o[3:0],c0);
191 
BCDSubAdjust u2 (hdN1,o[7:4],c1);
192 
BCDSubAdjust u3 (hdN2,o[11:8],c2);
193 
BCDSubAdjust u4 (hdN3,o[15:12],c);
194 
 
195 
endmodule
196 
 
197 
module BCDSubN(ci,a,b,o,co);
198 
parameter N=24;
199 
input ci;               // carry input
200 
input [N*4-1:0] a;
201 
input [N*4-1:0] b;
202 
output [N*4-1:0] o;
203 
output co;
204 
 
205 
genvar g;
206 
generate begin : gBCDSubN
207 
reg [4:0] hdN [0:N-1];
208 
wire [N:0] c;
209 
 
210 
assign c[0] = ci;
211 
assign co = c[N];
212 
 
213 
for (g = 0; g < N; g = g + 1)
214 
        always @*
215 
                hdN[g] = a[g*4+3:g*4] - b[g*4+3:g*4] - c[g];
216 
 
217 
for (g = 0; g < N; g = g + 1)
218 
        BCDSubAdjust u1 (hdN[g],o[g*4+3:g*4],c[g+1]);
219 
end
220 
endgenerate
221 
 
222 
endmodule
223 
 
224 
/*
225 
module BCDSub8NClk(clk, a, b, o, ci, co);
226 
parameter N=33;
227 
input clk;
228 
input [N*8-1:0] a;
229 
input [N*8-1:0] b;
230 
output [N*8-1:0] o;
231 
input ci;
232 
output co;
233 
 
234 
reg [N:0] c;
235 
wire [N:0] d;
236 
assign c[0] = ci;
237 
assign co = c[N];
238 
 
239 
genvar g;
240 
generate begin : gBCDsub
241 
for (g = 0; g < N; g = g + 1) begin
242 
        BCDSub u1 (c[g],a[g*8+7:g*8],b[g*8+7:g*8],o[g*8+7:g*8],d[g+1]);
243 
 
244 
        always_ff @(posedge clk)
245 
                c[g+1] <= d[g+1];
246 
end
247 
end
248 
endgenerate
249 
endmodule
250 
*/
251 
 
252 
module BCDAddAdjust(i,o,c);
253 
input [4:0] i;
254 
output [3:0] o;
255 
reg [3:0] o;
256 
output c;
257 
reg c;
258 
always @(i)
259 
case(i)
260 
5'h0: begin o = 4'h0; c = 1'b0; end
261 
5'h1: begin o = 4'h1; c = 1'b0; end
262 
5'h2: begin o = 4'h2; c = 1'b0; end
263 
5'h3: begin o = 4'h3; c = 1'b0; end
264 
5'h4: begin o = 4'h4; c = 1'b0; end
265 
5'h5: begin o = 4'h5; c = 1'b0; end
266 
5'h6: begin o = 4'h6; c = 1'b0; end
267 
5'h7: begin o = 4'h7; c = 1'b0; end
268 
5'h8: begin o = 4'h8; c = 1'b0; end
269 
5'h9: begin o = 4'h9; c = 1'b0; end
270 
5'hA: begin o = 4'h0; c = 1'b1; end
271 
5'hB: begin o = 4'h1; c = 1'b1; end
272 
5'hC: begin o = 4'h2; c = 1'b1; end
273 
5'hD: begin o = 4'h3; c = 1'b1; end
274 
5'hE: begin o = 4'h4; c = 1'b1; end
275 
5'hF: begin o = 4'h5; c = 1'b1; end
276 
5'h10:  begin o = 4'h6; c = 1'b1; end
277 
5'h11:  begin o = 4'h7; c = 1'b1; end
278 
5'h12:  begin o = 4'h8; c = 1'b1; end
279 
5'h13:  begin o = 4'h9; c = 1'b1; end
280 
default:        begin o = 4'h9; c = 1'b1; end
281 
endcase
282 
endmodule
283 
 
284 
module BCDSubAdjust(i,o,c);
285 
input [4:0] i;
286 
output [3:0] o;
287 
reg [3:0] o;
288 
output c;
289 
reg c;
290 
always @(i)
291 
case(i)
292 
5'h0: begin o = 4'h0; c = 1'b0; end
293 
5'h1: begin o = 4'h1; c = 1'b0; end
294 
5'h2: begin o = 4'h2; c = 1'b0; end
295 
5'h3: begin o = 4'h3; c = 1'b0; end
296 
5'h4: begin o = 4'h4; c = 1'b0; end
297 
5'h5: begin o = 4'h5; c = 1'b0; end
298 
5'h6: begin o = 4'h6; c = 1'b0; end
299 
5'h7: begin o = 4'h7; c = 1'b0; end
300 
5'h8: begin o = 4'h8; c = 1'b0; end
301 
5'h9: begin o = 4'h9; c = 1'b0; end
302 
5'h16: begin o = 4'h0; c = 1'b1; end
303 
5'h17: begin o = 4'h1; c = 1'b1; end
304 
5'h18: begin o = 4'h2; c = 1'b1; end
305 
5'h19: begin o = 4'h3; c = 1'b1; end
306 
5'h1A: begin o = 4'h4; c = 1'b1; end
307 
5'h1B: begin o = 4'h5; c = 1'b1; end
308 
5'h1C: begin o = 4'h6; c = 1'b1; end
309 
5'h1D: begin o = 4'h7; c = 1'b1; end
310 
5'h1E: begin o = 4'h8; c = 1'b1; end
311 
5'h1F: begin o = 4'h9; c = 1'b1; end
312 
default: begin o = 4'h9; c = 1'b1; end
313 
endcase
314 
endmodule
315 
 
316 
// Multiply two BCD digits
317 
// Method used is table lookup
318 
module BCDMul1(a,b,o);
319 
input [3:0] a;
320 
input [3:0] b;
321 
output [7:0] o;
322 
reg [7:0] o;
323 
 
324 
always @(a or b)
325 
casex({a,b})
326 
8'h00: o = 8'h00;
327 
8'h01: o = 8'h00;
328 
8'h02: o = 8'h00;
329 
8'h03: o = 8'h00;
330 
8'h04: o = 8'h00;
331 
8'h05: o = 8'h00;
332 
8'h06: o = 8'h00;
333 
8'h07: o = 8'h00;
334 
8'h08: o = 8'h00;
335 
8'h09: o = 8'h00;
336 
8'h10: o = 8'h00;
337 
8'h11: o = 8'h01;
338 
8'h12: o = 8'h02;
339 
8'h13: o = 8'h03;
340 
8'h14: o = 8'h04;
341 
8'h15: o = 8'h05;
342 
8'h16: o = 8'h06;
343 
8'h17: o = 8'h07;
344 
8'h18: o = 8'h08;
345 
8'h19: o = 8'h09;
346 
8'h20: o = 8'h00;
347 
8'h21: o = 8'h02;
348 
8'h22: o = 8'h04;
349 
8'h23: o = 8'h06;
350 
8'h24: o = 8'h08;
351 
8'h25: o = 8'h10;
352 
8'h26: o = 8'h12;
353 
8'h27: o = 8'h14;
354 
8'h28: o = 8'h16;
355 
8'h29: o = 8'h18;
356 
8'h30: o = 8'h00;
357 
8'h31: o = 8'h03;
358 
8'h32: o = 8'h06;
359 
8'h33: o = 8'h09;
360 
8'h34: o = 8'h12;
361 
8'h35: o = 8'h15;
362 
8'h36: o = 8'h18;
363 
8'h37: o = 8'h21;
364 
8'h38: o = 8'h24;
365 
8'h39: o = 8'h27;
366 
8'h40: o = 8'h00;
367 
8'h41: o = 8'h04;
368 
8'h42: o = 8'h08;
369 
8'h43: o = 8'h12;
370 
8'h44: o = 8'h16;
371 
8'h45: o = 8'h20;
372 
8'h46: o = 8'h24;
373 
8'h47: o = 8'h28;
374 
8'h48: o = 8'h32;
375 
8'h49: o = 8'h36;
376 
8'h50: o = 8'h00;
377 
8'h51: o = 8'h05;
378 
8'h52: o = 8'h10;
379 
8'h53: o = 8'h15;
380 
8'h54: o = 8'h20;
381 
8'h55: o = 8'h25;
382 
8'h56: o = 8'h30;
383 
8'h57: o = 8'h35;
384 
8'h58: o = 8'h40;
385 
8'h59: o = 8'h45;
386 
8'h60: o = 8'h00;
387 
8'h61: o = 8'h06;
388 
8'h62: o = 8'h12;
389 
8'h63: o = 8'h18;
390 
8'h64: o = 8'h24;
391 
8'h65: o = 8'h30;
392 
8'h66: o = 8'h36;
393 
8'h67: o = 8'h42;
394 
8'h68: o = 8'h48;
395 
8'h69: o = 8'h54;
396 
8'h70: o = 8'h00;
397 
8'h71: o = 8'h07;
398 
8'h72: o = 8'h14;
399 
8'h73: o = 8'h21;
400 
8'h74: o = 8'h28;
401 
8'h75: o = 8'h35;
402 
8'h76: o = 8'h42;
403 
8'h77: o = 8'h49;
404 
8'h78: o = 8'h56;
405 
8'h79: o = 8'h63;
406 
8'h80: o = 8'h00;
407 
8'h81: o = 8'h08;
408 
8'h82: o = 8'h16;
409 
8'h83: o = 8'h24;
410 
8'h84: o = 8'h32;
411 
8'h85: o = 8'h40;
412 
8'h86: o = 8'h48;
413 
8'h87: o = 8'h56;
414 
8'h88: o = 8'h64;
415 
8'h89: o = 8'h72;
416 
8'h90: o = 8'h00;
417 
8'h91: o = 8'h09;
418 
8'h92: o = 8'h18;
419 
8'h93: o = 8'h27;
420 
8'h94: o = 8'h36;
421 
8'h95: o = 8'h45;
422 
8'h96: o = 8'h54;
423 
8'h97: o = 8'h63;
424 
8'h98: o = 8'h72;
425 
8'h99: o = 8'h81;
426 
default:        o = 8'h00;
427 
endcase
428 
endmodule
429 
 
430 
 
431 
// Multiply two pairs of BCD digits
432 
// handles from 0x0 to 99x99
433 
module BCDMul2(a,b,o);
434 
input [7:0] a;
435 
input [7:0] b;
436 
output [15:0] o;
437 
 
438 
wire [7:0] p1,p2,p3,p4;
439 
wire [15:0] s1;
440 
 
441 
BCDMul1 u1 (a[3:0],b[3:0],p1);
442 
BCDMul1 u2 (a[7:4],b[3:0],p2);
443 
BCDMul1 u3 (a[3:0],b[7:4],p3);
444 
BCDMul1 u4 (a[7:4],b[7:4],p4);
445 
 
446 
BCDAdd4 u5 (1'b0,{p4,p1},{4'h0,p2,4'h0},s1);
447 
BCDAdd4 u6 (1'b0,s1,{4'h0,p3,4'h0},o);
448 
 
449 
endmodule
450 
 
451 
module BCDMul4(a,b,o);
452 
input [15:0] a;
453 
input [15:0] b;
454 
output [31:0] o;
455 
 
456 
wire [15:0] p1,p2,p3,p4;
457 
wire [31:0] s1;
458 
 
459 
BCDMul2 u1 (a[7:0],b[7:0],p1);
460 
BCDMul2 u2 (a[15:8],b[7:0],p2);
461 
BCDMul2 u3 (a[7:0],b[15:8],p3);
462 
BCDMul2 u4 (a[15:8],b[15:8],p4);
463 
 
464 
BCDAddN #(.N(8)) u5 (1'b0,{p4,p1},{8'h0,p2,8'h0},s1);
465 
BCDAddN #(.N(8)) u6 (1'b0,s1,{8'h0,p3,8'h0},o);
466 
 
467 
endmodule
468 
 
469 
module BCDMul8(a,b,o);
470 
input [31:0] a;
471 
input [31:0] b;
472 
output [63:0] o;
473 
 
474 
wire [31:0] p1,p2,p3,p4;
475 
wire [63:0] s1;
476 
 
477 
BCDMul4 u1 (a[15:0],b[15:0],p1);
478 
BCDMul4 u2 (a[31:16],b[15:0],p2);
479 
BCDMul4 u3 (a[15:0],b[31:16],p3);
480 
BCDMul4 u4 (a[31:16],b[31:16],p4);
481 
 
482 
BCDAddN #(.N(16)) u5 (1'b0,{p4,p1},{16'h0,p2,16'h0},s1);
483 
BCDAddN #(.N(16)) u6 (1'b0,s1,{16'h0,p3,16'h0},o);
484 
 
485 
endmodule
486 
 
487 
module BCDMul16(a,b,o);
488 
input [63:0] a;
489 
input [63:0] b;
490 
output [127:0] o;
491 
 
492 
wire [63:0] p1,p2,p3,p4;
493 
wire [127:0] s1;
494 
 
495 
BCDMul8 u1 (a[31:0],b[31:0],p1);
496 
BCDMul8 u2 (a[63:32],b[31:0],p2);
497 
BCDMul8 u3 (a[31:0],b[63:32],p3);
498 
BCDMul8 u4 (a[63:32],b[63:32],p4);
499 
 
500 
BCDAddN #(.N(32)) u5 (1'b0,{p4,p1},{32'h0,p2,32'h0},s1);
501 
BCDAddN #(.N(32)) u6 (1'b0,s1,{32'h0,p3,32'h0},o);
502 
 
503 
endmodule
504 
 
505 
module BCDMul32(a,b,o);
506 
input [127:0] a;
507 
input [127:0] b;
508 
output [255:0] o;
509 
 
510 
wire [127:0] p1,p2,p3,p4;
511 
wire [255:0] s1;
512 
 
513 
BCDMul16 u1 (a[63:0],b[63:0],p1);
514 
BCDMul16 u2 (a[127:64],b[63:0],p2);
515 
BCDMul16 u3 (a[63:0],b[127:64],p3);
516 
BCDMul16 u4 (a[127:64],b[127:64],p4);
517 
 
518 
BCDAddN #(.N(64)) u5 (1'b0,{p4,p1},{64'h0,p2,64'h0},s1);
519 
BCDAddN #(.N(64)) u6 (1'b0,s1,{64'h0,p3,64'h0},o);
520 
 
521 
endmodule
522 
 
523 
module BCDMul_tb();
524 
 
525 
wire [15:0] o1,o2,o3,o4;
526 
 
527 
BCDMul2 u1 (8'h00,8'h00,o1);
528 
BCDMul2 u2 (8'h99,8'h99,o2);
529 
BCDMul2 u3 (8'h25,8'h18,o3);
530 
BCDMul2 u4 (8'h37,8'h21,o4);
531 
 
532 
endmodule
533 
 
534 
module BinToBCD(i, o);
535 
input [7:0] i;
536 
output [11:0] o;
537 
 
538 
reg [11:0] tbl [0:255];
539 
 
540 
genvar g;
541 
generate begin : gTbl
542 
reg [3:0] n0 [0:255];
543 
reg [3:0] n1 [0:255];
544 
reg [3:0] n2 [0:255];
545 
 
546 
for (g = 0; g < 256; g = g + 1) begin
547 
        initial begin
548 
                n0[g] = g % 10;
549 
                n1[g] = g / 10;
550 
                n2[g] = g / 100;
551 
                tbl[g] <= {n2[g],n1[g],n0[g]};
552 
        end
553 
end
554 
 
555 
assign o = tbl[i];
556 
 
557 
end
558 
endgenerate
559 
 
560 
endmodule
561 
 
562 
// Perform a logical shift to the right.
563 
module BCDSRL(ci, i, o, co);
564 
parameter N=4;
565 
input ci;
566 
input [N*4-1:0] i;
567 
output reg [N*4-1:0] o;
568 
output co;
569 
 
570 
reg [N:0] c;
571 
 
572 
genvar g;
573 
generate begin
574 
always @*
575 
        c[N] = ci;
576 
for (g = N - 1; g >= 0; g = g - 1)
577 
always @*
578 
        c[g] = i[g*4];
579 
for (g = N - 1; g >= 0; g = g - 1)
580 
always @*
581 
begin
582 
        o[g*4+3:g*4] = {1'b0,i[g*4+3:g*4+1]};
583 
        // Because there is a divide by two, the value will range between 0 and 4.
584 
        // Adding 5 keeps it within deicmal boundaries of 0 to 9. No carry can be
585 
        // generated
586 
        if (c[N+1])
587 
                o[g*4+3:g*4] = o[g*4+3:g*4] + 4'd5;
588 
end
589 
        assign co = c[0];
590 
end
591 
endgenerate
592 
 
593 
endmodule

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