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Note for Digital System Design - DSD By Yared Getahun

• Digital System Design - DSD
• Note
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Unit IV Digital Systems Basic Logic Circuit Concepts

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Basic Definitions  Binary Operators ● AND z=x•y=xy z=1 if x=1 AND y=1 ● OR z=x+y z=1 if x=1 OR y=1 ● NOT z = x = x’ z=1 if x=0  Boolean Algebra ● Binary Variables: only ‘0’ and ‘1’ values ● Algebraic Manipulation

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Boolean Algebra Postulates  Commutative Law x•y=y•x x+y=y+x  Identity Element x•1=x x+0=x  Complement x • x’ = 0 x + x’ = 1

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Boolean Algebra Theorems  Duality ● The dual of a Boolean algebraic expression is obtained by interchanging the AND and the OR operators and replacing the 1’s by 0’s and the 0’s by 1’s. ● x•(y+z)=(x•y)+(x•z) ● x+(y•z)=(x+y)•(x+z)  Theorem 1 ● x•x=x x+x=x  Theorem 2 ● x•0=0 x+1=1 Applied to a valid equation produces a valid equation