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