lec11Adders - Introduction to CMOS VLSI Design Adders...

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Introduction to CMOS VLSI Design Adders
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Adders Slide 2 CMOS VLSI Design Outline Single-bit Addition Carry-Ripple Adder Carry-Skip Adder Carry-Lookahead Adder Carry-Select Adder Carry-Increment Adder Tree Adder
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Adders Slide 3 CMOS VLSI Design Single-Bit Addition Half Adder Full Adder A B C out S 0 0 0 1 1 0 1 1 A B C C out S 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B S C out A B C S C out out S C = = out S C = =
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Adders Slide 4 CMOS VLSI Design Single-Bit Addition Half Adder Full Adder A B C out S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 A B C C out S 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 A B S C out A B C S C out out S A B C A B = = g out ( , , ) S A B C C MAJ A B C = =
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Adders Slide 5 CMOS VLSI Design PGK For a full adder, define what happens to carries – Generate: C out = 1 independent of C G = – Propagate: C out = C P = – Kill: C out = 0 independent of C K =
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Adders Slide 6 CMOS VLSI Design PGK For a full adder, define what happens to carries – Generate: C out = 1 independent of C G = A • B – Propagate: C out = C P = A B – Kill: C out = 0 independent of C K = ~A • ~B
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Adders Slide 7 CMOS VLSI Design Full Adder Design I Brute force implementation from eqns out ( , , ) S A B C C MAJ A B C = = A B C S C out MAJ A B C A B B B A C S C C C B B B A A A B C B A C B A A B C C out C A A B B
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Adders Slide 8 CMOS VLSI Design Full Adder Design II Factor S in terms of C out S = ABC + (A + B + C)(~C out ) Critical path is usually C to C out in ripple adder S S C out A B C C out MINORITY
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Adders Slide 9 CMOS VLSI Design Layout Clever layout circumvents usual line of diffusion Use wide transistors on critical path Eliminate output inverters
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Adders Slide 10 CMOS VLSI Design Full Adder Design III Complementary Pass Transistor Logic (CPL) Slightly faster, but more area A C S S B B C C C B B C out C out C C C C B B B B B B B B A A A
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Adders Slide 11 CMOS VLSI Design Full Adder Design IV Dual-rail domino Very fast, but large and power hungry Used in very fast multipliers C out _h A_h B_h C_h B_h A_h φ C out _l A_l B_l C_l B_l A_l φ S_h S_l A_h B_h B_h B_l A_l C_l C_h C_h φ
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Adders Slide 12 CMOS VLSI Design Carry Propagate Adders N-bit adder called CPA Each sum bit depends on all previous carries How do we compute all these carries quickly? + B N...1 A N...1 S N...1 C in C out 11111 1111 +0000 0000 A 4...1 carries B 4...1 S 4...1 C in C out 00000 1111 +0000 1111 C in C out
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Adders Slide 13 CMOS VLSI Design Carry-Ripple Adder Simplest design: cascade full adders Critical path goes from Cin to Cout Design full adder to have fast carry delay C in C out B 1 A 1 B 2 A 2 B 3 A 3 B 4 A 4 S 1 S 2 S 3 S 4 C 1 C 2 C 3
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Adders Slide 14 CMOS VLSI Design Inversions Critical path passes through majority gate Built from minority + inverter Eliminate inverter and use inverting full adder C out C in B 1 A 1 B 2 A 2 B 3 A 3 B 4 A 4 S 1 S 2 S 3 S 4 C 1 C 2 C 3
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lec11Adders - Introduction to CMOS VLSI Design Adders...

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