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L5 Combinational Cir - Lecture 5 Combination Circuit Digital Design Copyright 2007 Frank Vahid 1 Combinational Logic Design Process Step 2.7

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1 Digital Design Copyright © 2007 Frank Vahid Lecture 5 Combination Circuit
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2 Digital Design Copyright © 2007 Frank Vahid Combinational Logic Design Process Step Description Step 1 Capture the function Create a truth table or equations, whichever is most natural for the given problem , to describe the desired behavior of the combinational logic. Step 2 Convert to equations This step is only necessary if you captured the function using a truth table instead of equations. Create an equation for each output by ORing all the minterms for that output. Simplify the equations if desired. Step 3 Implement as a gate- based circuit For each output, create a circuit corresponding to the output’s equation. (Sharing gates among multiple outputs is OK optionally.) 2.7
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3 Digital Design Copyright © 2007 Frank Vahid Example: Number of 1s Count • Problem: Output in binary on two outputs yz the number of 1s on three inputs • 010 Æ 01 101 Æ 10 000 Æ 00 Step 1: Capture the function • Truth table or equation? – Truth table is straightforward Step 2: Convert to equation • y = a’bc + ab’c + abc’ + abc • z = a’b’c + a’bc’ + ab’c’ + abc Step 3: Implement as a gate- based circuit a b c a b c a b c a b c z a b c a b c a b y
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4 Digital Design Copyright © 2007 Frank Vahid Half Adder Based on the operations it performs, a truth table can be built Derive Boolean functions (canonical forms) from the truth table for both outputs Sum = A’B + AB’ = m1 + m2 = Σ (1, 2) = (A+B)(A’+B’) = M0•M3 = Π (0, 3) Carry = AB = m3 = (A+B)(A+B’)(A’+B) = M0•M1•M2 = Π (0, 1, 2) A B Carry Sum 0 1 1 0 Sum 1 1 1 0 0 1 0 1 0 0 0 0 Carry B A Half-Adder A B Carry Sum
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5 Digital Design Copyright © 2007 Frank Vahid Full Adder Based on the operations it performs, a truth table can be built Derive minterm/Maxterm expressions from the truth table for both outputs Sum = ? Carry = ? 1 Sum 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 Carry C B A Full-Adder A B Carry Sum C Logic Circuit?
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6 Digital Design Copyright © 2007 Frank Vahid Full Adder 1 0 0 1 0 1 1 0 Sum 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 Carry C B A Full-Adder A B Carry Sum C Sum = A’B’C + A’BC’ + AB’C’ + ABC = Σ m(1, 2, 4, 7) Carry = A’BC + AB’C + ABC’ + ABC = Σ m(3, 5, 6, 7) Sum Carry Notice the circuit draw convention
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This note was uploaded on 10/14/2011 for the course EE 270/370 taught by Professor Gangzheng during the Fall '11 term at Shanghai Jiao Tong University.

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L5 Combinational Cir - Lecture 5 Combination Circuit Digital Design Copyright 2007 Frank Vahid 1 Combinational Logic Design Process Step 2.7

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