05 Combinational Functional Blocks

# 05 Combinational Functional Blocks - 1 EE2000 Logic Circuit...

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Unformatted text preview: 1 EE2000 Logic Circuit Design 5 Combinational Function Blocks Â¡ Â¡ Â¡ Â¡ 2 Outline Â¡ 5.1 Building Larger Circuits Â¡ 5.2 Arithmetic Combinational Functional Blocks Â¡ Adders, Subtractors Â¡ Half Adders, Full Adders, Ripple Carry Adders Â¡ 5.3 Logical Combinational Functional Blocks Â¡ Decoders, with and without Enabling Â¡ Encoders, with Priority Â¡ Multiplexers Â¡ Demultiplexers Â¡ 5.4 Programmable Logic Devices Â¡ ROM, PLA, PAL 3 5.1 Building Larger Circuits 4 Example Â¡ Design a logic circuit that perform an equality comparator A E Output Inputs B ? 5 1-bit Equality Comparator Â¡ Specification: Â¡ A circuit to compare two binary numbers to determine whether they are equal or not Â¡ The inputs consist of two numbers: A and B Â¡ Each number consists of 1-bit namely A and B Â¡ The output of the circuit is a 1-bit variable E Â¡ E is equal to 1 if A and B are equal Â¡ E will be 0 if A and B are unequal 6 1-bit Equality Comparator Â¡ Formulation: Â¡ Optimization: Â¡ E ( A , B ) = Î£ m (0, 4) Â¡ = A â€™ B â€™ + A B Â¡ = A âŠ— B Â¡ Final logic diagram: Inputs Output A B E 1 1 1 1 1 1 A B E A B E or 7 2-bit Equality Comparator Â¡ How to design a 2-bit equality comparator? Â¡ Specification: Â¡ The inputs consist of two 2-bit numbers : A ( A 1 A ) and B ( B 1 B ) Â¡ E is equal to 1 if A and B are equal (MSB) (LSB) A E Output Inputs B 1 A 1 B ? (MSB) (LSB) 8 2-bit Equality Comparator Â¡ Formulation: Â¡ How many inputs? Â¡ How many outputs? Â¡ How many rows? Â¡ Optimization: Â¡ E ( A 1 , A , B 1 , B ) Â¡ = Î£ m (0, 5, 10, 15) Â¡ = A 1 â€™ A â€™ B 1 â€™ B â€™ + Â¡ A 1 â€™ A B 1 â€™ B + A 1 A â€™ B 1 B â€™ Â¡ + A 1 A B 1 B Inputs Output A 1 A B 1 B E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 4-bit Equality Comparator Â¡ How to design a 4-bit equality comparator? Â¡ Specification: Â¡ The inputs consist of two 4-bit numbers : A ( A 3 A 2 A 1 A ) and B ( B 3 B 2 B 1 B ) Â¡ E is equal to 1 if A and B are equal (MSB) (LSB) A E Output Inputs B 1 A 1 B (MSB) (LSB) A 2 A 3 B 3 B 2 ? 10 4-bit Equality Comparator Â¡ Formulation: Â¡ How many inputs? Â¡ How many outputs? Â¡ How many rows? Inputs Output A 3 A 2 A 1 A B 3 B 2 B 1 B E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 Problems Â¡ Problems Â¡ Not feasible (too many rows in the truth table) Â¡ Even if list all combinations in the truth table, cannot use K-map to simplify them (why?) Â¡ Solution: Â¡ Modular design is suggested Â¡ Circuit broken up into pieces called blocks Â¡ If block is still too large and complex to be designed, broken into smaller blocks Â¡ Each block should work independently 12 Modular Design Â¡ Circuit broken up into pieces called blocks Â¡ Decompose the problem into four 1-bit comparison circuits Â¡ Compare bit by bit, then combine all results Â¡ The new logic diagram E A 3 B 3 A 2 B 2 A 1 B 1 A B Functional Blocks: 1-bit Comparator Block Equality Block ?...
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05 Combinational Functional Blocks - 1 EE2000 Logic Circuit...

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