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ch_10_probs

# ch_10_probs - CHAPTER Combinational Logic I Boolean Algebra...

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223 CHAPTER 10 Combinational Logic I: Boolean Algebra :

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224 Chapter 10: Combinational Logic I: Boolean Algebra CHAPTER 10: PROBLEMS S 10.1 Prove the equivalence of the following Boolean Identity (i.e. show that the left side equals the right under the Laws of Bool- ean Algebra). Perform only one manipulation per line, and mark the number of the Boolean Algebra rule you used for that line from the table on page 230 of your textbook. 10.2 Consider the following truth table for a boolean function F, taking 3 inputs, A, B and C. (a) Determine the Boolean expression for F. (b) Reduce F using the rules from page 230. (c) Implement F using gates. You may use any type of gate cov- ered in the text. 10.3 Consider the following boolean expression. A B C F 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 B AD + BC DD ABCD BCD BC ACD ACD + + + + + + = F ABC A BC CB + + + ( ) A CA + ( ) =
225 Digital Electronics (a) Draw the circuit using only inverters, 2 input AND and 2 input OR gates. (b) Reduce the expression using the rules of Boolean Algebra. (c) Now draw the reduced circuit using only inverters, 2 input AND and 2 input OR gates. 10.4 Simplify the following expression using the axioms and theo- rems of Boolean Algebra. Note which axiom or theorem you use for each step from the table on page 230. (a) (b) (c) 10.5 Consider the following Boolean Functions. (a) Use the axioms and theorems of Boolean Algebra to sim- plify the following expression. Be sure to note which axiom or theorem used at each stage of your reduction from the table on page 230.

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