A Novel Graphical Technique for Combinational Logic Representation and Optimization

<div>“NAND-only” implementation of the newly defined logical operations “<svg height="6.01072pt" id="M195" style="vertical-align:-0.04980993pt" version="1.1" viewbox="-0.0498162 -5.96091 7.75925 6.01072" width="7.75925pt" 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="M506 291L495 327L324 283L313 459H275L264 283L94 327L82 291L246 227L151 78L182 56L294 192L406 56L437 78L342 227L506 291Z" id="g113-44"></path></g></svg> and <svg height="9.29902pt" id="M196" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -9.24921 7.75925 9.29902" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.763,-.222)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z" id="g119-25"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M506 291L495 327L324 283L313 459H275L264 283L94 327L82 291L246 227L151 78L182 56L294 192L406 56L437 78L342 227L506 291Z" id="g113-44"></path></g></svg>” that are essentially <svg height="7.35473pt" id="M197" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" 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="M573 255C573 407 448 530 294 530S15 407 15 255S140 -20 294 -20S573 103 573 255ZM520 280H323V484C426 471 508 386 520 280ZM265 280H68C80 386 162 471 265 484V280ZM265 26C162 39 80 124 68 230H265V26ZM520 230C508 124 426 39 323 26V230H520Z" id="g117-68"></path></g></svg> (XOR) and <svg height="7.35473pt" id="M198" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" 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="M573 255C573 407 448 530 294 530S15 407 15 255S140 -20 294 -20S573 103 573 255ZM521 255C521 127 419 24 294 24S67 127 67 255S169 486 294 486S521 383 521 255ZM350 255C350 288 326 313 294 313S238 288 238 255C238 220 262 197 294 197S350 220 350 255Z" id="g117-72"></path></g></svg> (XNOR) operations, respectively, for a two-input system.</div>

Complexity

fig5

Figure 5

Figure 5: A Novel Graphical Technique for Combinational Logic Representation and Optimization 