(Combinational Logic Circuit)

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(Combinational Logic Circuit) Computer Engineering (Logic Circuits) Lec. # 9 (Combinational Logic Circuit) Dr. Tamer Samy Gaafar Dept. of Computer & Systems Engineering Faculty of Engineering Zagazig University

Course Web Page http://www.tsgaafar.faculty.zu.edu.eg Email: tsgaafar@yahoo.com

Combinational Logic Circuits (Contd.) Lec. # 9 Ch. 4 Combinational Logic Circuits (Contd.)

Only one switch should be activated at a time Encoders Put “Information” into code Binary Encoder Example: 4-to-2 Binary Encoder Only one switch should be activated at a time X0 Binary Encoder 1 x3 x2 x1 x0 y1 y0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 x1 x2 x3 y1 y0 2 3

Encoders Octal-to-Binary Encoder (8-to-3) Binary Encoder Y2 Y1 Y0 I7 I4 I3 I2 I1 I0 I7 I6 I5 I4 I3 I2 I1 I0 Y2 Y1 Y0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1

Priority Encoders 4-Input Priority Encoder Priority Encoder V0 Y1 Y0 I3 I2 I1 I0 Y1 Y0 V 0 0 0 0 0 0 0 0 0 1 1 0 0 1 x 0 1 0 1 x x 1 0 1 x x x 1 1 Y1 I1 1 I2 I3 I0

Encoder / Decoder Pairs Binary Encoder Binary Decoder I7 I6 I5 I4 I3 I2 I1 I0 Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0 7 7 6 6 5 5 Y2 Y1 Y0 I2 I1 I0 4 4 3 3 2 2 1 1

Multiplexers S1 S0 Y 0 0 I0 0 1 I1 1 0 I2 1 1 I3 MUX Y I0 I1 I2 I3 0 0 I0 0 1 I1 1 0 I2 1 1 I3 MUX Y I0 I1 I2 I3 S1 S0

Multiplexers 2-to-1 MUX 4-to-1 MUX I0 MUX I1 Y S I0 I1 MUX I2 I3 Y S1 S0

Multiplexers Quad 2-to-1 MUX x3 y3 x2 y2 x1 y1 x0 y0 I0 MUX I1 Y S Y3 AA S E Y3 Y2 Y1 Y0 B3 B2 B1 B0 S

Multiplexers Quad 2-to-1 MUX A3 A2 A1 A0 MUX Y3 Y2 Y1 Y0 B3 B2 B1 B0 S E Y3 Y2 Y1 Y0 B3 B2 B1 B0 Extra Buffers

Implementation Using Multiplexers Example F(x, y) = ∑(0, 1, 3) x y F 0 0 1 0 1 1 0 1 1 MUX Y I0 I1 I2 I3 S1 S0 1 F x y

Implementation Using Multiplexers Example F(x, y, z) = ∑(1, 2, 6, 7) MUX Y I0 I1 I2 I3 I4 I5 I6 I7 S2 S1 S0 1 x y z F 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 F x y z

Implementation Using Multiplexers Example F(x, y, z) = ∑(1, 2, 6, 7) x y z F 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 MUX Y I0 I1 I2 I3 S1 S0 z F = z F z F = z 1 F = 0 x y F = 1

Implementation Using Multiplexers Example F(A, B, C, D) = ∑(1, 3, 4, 11, 12, 13, 14, 15) A B C D F 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 MUX Y I0 I1 I2 I3 I4 I5 I6 I7 S2 S1 S0 D F = D D F = D D F = D F F = 0 D F = 0 1 F = D 1 F = 1 F = 1 A B C

Multiplexer Expansion 8-to-1 MUX using Dual 4-to-1 MUX MUX Y I0 I1 I2 I3 S1 S0 Y I0 I1 I2 I3 I4 I5 I6 I7 S2 S1 S0 MUX Y I0 I1 S MUX Y I0 I1 I2 I3 S1 S0 1 0 0

DeMultiplexers DeMUX I Y3 Y2 Y1 Y0 S1 S0 S1 S0 Y3 Y2 Y1 Y0 0 0 I 0 1 0 0 I 0 1 1 0 1 1

Multiplexer / DeMultiplexer Pairs MUX DeMUX Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0 7 I7 I6 I5 I4 I3 I2 I1 I0 7 6 6 5 5 4 4 Y I 3 3 2 2 1 1 S2 S1 S0 S2 S1 S0 Synchronize x2 x1 x0 y2 y1 y0

DeMultiplexers / Decoders DeMUX I Y3 Y2 Y1 Y0 S1 S0 Binary Decoder I1 I0 E Y3 Y2 Y1 Y0 E I1 I0 Y3 Y2 Y1 Y0 x x 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 S1 S0 Y3 Y2 Y1 Y0 0 0 I 0 1 1 0 1 1

Seven-Segment Decoder a b c g e d f w x y z a b c d e f g 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 x x x x x x x 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 ? w x y z a b c d e f g BCD code y 1 x w z b = . . . a = w + y + xz + x’z’ c = . . . d = . . .

Three-State Gates Tri-State Buffer Tri-State Inverter C A Y 0 x Hi-Z 1 0 1 1 1 A Y C A Y C

Three-State Gates C D Y 0 0 Hi-Z 0 1 B 1 0 A 1 1 ? A Y C B Not Allowed 0 0 Hi-Z 0 1 B 1 0 A 1 1 ? A Y C B Not Allowed D A C B A if C = 1 B if C = 0 Y=

Three-State Gates Binary Decoder I3 I2 Y I1 I0 Y3 Y2 S1 I1 I0 Y1 E Y0

Binary Multipliers

Binary Multiplier

Binary Multiplier

Binary Multiplier

4 bit by 3 bit Binary Multiplier

4 bit by 3 bit Binary Multiplier