ch6_Functions of Combinational Logic

ch6_Functions of Combinational Logic - Ch.6 Functions of...

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Ch.6 Functions of Combination Logic Basi c Adder s Par al l el Bi nar y Adder s Compar at or s Decoder s Encoder s Code Conver t er s Mul t i pl exer s( Dat a Sel ect or s) Demul t i pl exer s Par i t y Gener at or s/ Checker s Tr oubl eshoot i ng Pr ogr ammabl e Logi c: The FPGA Logi c Funct i ons wi t h VHDL
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2 Information Security Lab. I nt r oduct i on f n m Y=f(X) X X: thefiniteset of input symbols Y: thefiniteset of output symbols f: a Boolean function for theoutput Digital Logic (1) Combinational Logic Circuit, (2) Sequential Logic Circuit Combinational Logic Circuit
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3 Information Security Lab. Sequential Logic Circuit Latches, Flip-flops RAM, etc.
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4 Information Security Lab. Basi c Adders TheHalf-Adder A + B = Σ (sum) and a carry Σ = A B Carry = AB This is logic not math 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 Car r y Σ B A
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5 Information Security Lab. The Ful l - Adder The f ul l Adder has a Car r y I n 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 Σ C out C i n B A Full Adder Logic Σ = (A B)’C in + (A B )C’ in or Σ = (A B) C in C out = AB + (A B) C in
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6 Information Security Lab.
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7 Information Security Lab. Ful l Adder
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8 Information Security Lab. Figure 6-5 Full-adder implemented with half-adders.
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9 Information Security Lab. I mpl ement at i on of Ful l Adder i n Sum of Pr oduct s
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10 Information Security Lab. Paral l el Bi nar y Adders 1 1 1 + 0 1 1 0 0 In this case, the carry bit from second column becomes a sum bit Carry bit from right column
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11 Information Security Lab. Bi t Par al l el Adder Ripple carry : carry propagation delay Look-ahead carry
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12 Information Security Lab. Adder Expansi on: 16 bi t adder
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13 Information Security Lab. Bi nar y Ri ppl e Car r y Adder Input Carry 0110 Augend A 1011 Addend B 0011 Sum S 1110 Output Carry 0011
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14 Information Security Lab. Fi gur e A- 2 Four - bi t par al l el adder s.
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15 Information Security Lab. Fi gur e A- 3 Char act er i st i cs f or t he 74LS283.
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16 Information Security Lab. Ex 6- 4) Show how t wo 4- bi t par al l el adder s can be connect ed t o f or m an 8- bi t par al l el adder. Show out put bi t s f or t he f ol l owi ng 8- bi t i nput number s: A 8 A 7 A 6 A 5 A 4 A 3 A 2 A 1 =1011 1001 and B 8 B 7 B 6 B 5 B 4 B 3 B 2 B 1 =1001 1110 Sol )
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17 Information Security Lab. I n n- bi t r i ppl e car r y adder : 2n( or 2n+2) gat e del ays r educe t he gat e del ays Look- ahead Car y Par t i al Ful l Adder ( PFA) pr opagat e f unct i on : P i =A i B i gener at e f unct i on : G i =A i B i Sum : S i =P i C i Car r y : C i +1 =G i + P i C i S i C i +1 C i A i B i P i G i Car r y Look- ahead Adder
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18 Information Security Lab. C 1 =G 0 +P 0 C 0 C 2 =G 1 +P 1 C 1 = G 1 +P 1 ( G 0 +P 0 C 0 ) = G 1 + P 1 G 0 + P 1 P 0 C 0 C 3 =G 2 +P 2 C 2 = G 2 +P 2 G 1 +P 2 P 1 G 0 + P 2 P 1 P 0 C 0 C 4 =G 3 +P 3 C 3 = G 3 +P 3 G 2 +P 3 P 2 G 1 + P 3 P 2 P 1 G 0 + P 3 P 2 P 1 P 0 C 0 • • • • • • • • • • • • • • • • • • C i =G i - 1 +P i - 1 G i - 2 + P i - 1 P i - 2 G i - 3 + • • + P i - 1 • • P 2 G 0 + P i - 1 • • P 1 P 0 C 0
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19 Information Security Lab.
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20 Information Security Lab.
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