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Logic Design

Logic Design . Safwan Mawlood Digital Principles and Logic Design . ADDERS. Gate Design constraints . (1) minimum number of gates, (2) minimum number of outputs, (3) minimum propagation time of the signal through a circuit, (4)minimum number of interconnections, and

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Logic Design

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  1. Logic Design Safwan Mawlood Digital Principles and Logic Design ADDERS

  2. Gate Design constraints • (1) minimum number of gates, • (2) minimum number of outputs, • (3) minimum propagation time of the signal through a circuit, • (4)minimum number of interconnections, and • (5) limitations of the driving capabilities of each logic gate.

  3. Addition of two binary digits is the simple addition consists of four possible elementary operations, which are 0+0 = 0, 0+1 = 1, 1+0 = 1, and 1+1 = 10. The first three operations produce a sum of one digit, but the fourth operation produces a sum consisting of two digits. The higher significant bit of this result is called the carry. • A combinational circuit that performs the addition of two bits is called a half-adder

  4. The truth table

  5. The Boolean Expression

  6. Logic Diagram for Half-adder

  7. Full Adder • When the augend and addend numbers contain more significant digits, the carry obtained from the addition of two bits is added to the next higher-order pair of significant bits. Here the • addition operation involves three bits—the augend bit, addend bit, and the carry bit and • produces a sum result as well as carry. The combinational circuit performing this type of • addition operation is called a full-adder

  8. The truth table

  9. The Boolean Expression

  10. Logic Diagram for Full-adder

  11. Karnaugh map • Example 4.3. Simplify the expression F = A'B'C + A'BC + A'BC' + AB'C + ABC. • Solution. The Karnaugh map is shown The four adjacent squares comprising the main terms A'B'C, A'BC, AB'C, and ABC can be combined. Here, it may observed that two of the variables A and B are changing their forms form uncomplemented to complemented. Therefore, these variables can be removed to form the reduced expression to C.

  12. F = C + A'B

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