First Steps in Creating Online Testable Reversible Sequential Circuits

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Present state</td><td class="align_center">Next state</td><td class="align_center">Modified next state</td></tr><tr class="thead"><td class="align_left"><span style="width: 80.6234ptpx;"><svg height="10.7866pt" id="M169" style="vertical-align:-2.150701pt" version="1.1" viewbox="-0.0498162 -8.6359 80.6234 10.7866" width="80.6234pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path></g><g 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381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path></g><g transform="matrix(.013,0,0,-0.013,74.502,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,80.742,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">00000</td><td class="align_center"> 0000</td><td class="align_center"> 0000</td></tr><tr><td class="align_left">00001</td><td class="align_center"> 0000</td><td class="align_center"> 0001</td></tr><tr><td class="align_left">00010</td><td class="align_center"> 0001</td><td class="align_center"> 0011</td></tr><tr><td class="align_left">00011</td><td class="align_center"> 0001</td><td class="align_center"> 0010</td></tr><tr><td class="align_left">00100</td><td class="align_center"> 0010</td><td class="align_center"> 0110</td></tr><tr><td class="align_left">00101</td><td class="align_center"> 0010</td><td class="align_center"> 0111</td></tr><tr><td class="align_left">00110</td><td class="align_center"> 0011</td><td class="align_center"> 0101</td></tr><tr><td class="align_left">00111</td><td class="align_center"> 0011</td><td class="align_center"> 0100</td></tr><tr><td class="align_left">01000</td><td class="align_center"> 0100</td><td class="align_center"> 1100</td></tr><tr><td class="align_left">01001</td><td class="align_center"> 0100</td><td class="align_center"> 1101</td></tr><tr><td class="align_left">01010</td><td class="align_center"> 0101</td><td class="align_center"> 1111</td></tr><tr><td class="align_left">01011</td><td class="align_center"> 0101</td><td class="align_center"> 1110</td></tr><tr><td class="align_left">01100</td><td class="align_center"> 0110</td><td class="align_center"> 1010</td></tr><tr><td class="align_left">01101</td><td class="align_center"> 0110</td><td class="align_center"> 1011</td></tr><tr><td class="align_left">01110</td><td class="align_center"> 0111</td><td class="align_center"> 1001</td></tr><tr><td class="align_left">01111</td><td class="align_center"> 0111</td><td class="align_center"> 1000</td></tr><tr><td class="align_left">10000</td><td class="align_center"> 1000</td><td class="align_center"> 1000</td></tr><tr><td class="align_left">10001</td><td class="align_center"> 1000</td><td class="align_center"> 1001</td></tr><tr><td class="align_left">10010</td><td class="align_center"> 1001</td><td class="align_center"> 1011</td></tr><tr><td class="align_left">10011</td><td class="align_center"> 1001</td><td class="align_center"> 1010</td></tr><tr><td class="align_left">10100</td><td class="align_center"> 1010</td><td class="align_center"> 1110</td></tr><tr><td class="align_left">10101</td><td class="align_center"> 1010</td><td class="align_center"> 1111</td></tr><tr><td class="align_left">10110</td><td class="align_center"> 1011</td><td class="align_center"> 1101</td></tr><tr><td class="align_left">10111</td><td class="align_center"> 1011</td><td class="align_center"> 1100</td></tr><tr><td class="align_left">11000</td><td class="align_center"> 1100</td><td class="align_center"> 0100</td></tr><tr><td class="align_left">11001</td><td class="align_center"> 1100</td><td class="align_center"> 0101</td></tr><tr><td class="align_left">11010</td><td class="align_center"> 1101</td><td class="align_center"> 0111</td></tr><tr><td class="align_left">11011</td><td class="align_center"> 1101</td><td class="align_center"> 0110</td></tr><tr><td class="align_left">11100</td><td class="align_center"> 1110</td><td class="align_center"> 0010</td></tr><tr><td class="align_left">11101</td><td class="align_center"> 1110</td><td class="align_center"> 0011</td></tr><tr><td class="align_left">11110</td><td class="align_center"> 1111</td><td class="align_center"> 0001</td></tr><tr><td class="align_left">11111</td><td class="align_center"> 1111</td><td class="align_center"> 0000</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Truth table representing the next states and the modified next states of a four-bit serial-in serial-out right-shift register [<a href="/journals/vlsi/2018/6153274/#B43" target="_blank">43</a>].

VLSI Design

tab5

Table 5

Table 5: First Steps in Creating Online Testable Reversible Sequential Circuits 