Running head: BOOLEAN ALGEBRA1Boolean Algebra and Number SystemsStudents NameInstitutional AffiliationBOOLEAN ALGEBRA2Boolean Algebra and Number Systems1. Simplify the following Boolean expression: AB(A + B)(C + C)AB(A + B)(C + C)= (ABA + ABB)(C)Considering that A.A=A, B.B=B, and C+C=C= (AB + AB)C= ABC2. Design the combinatorial circuit for: (p *r) + qpNOTANDrqOR3. Design the combinatorial circuit for:pANDNOTORqORrANDsBOOLEAN ALGEBRA34. Complete the truth table of the following Boolean expression:It is 3 input, therefore the table has 2^3 = 8 rows.p11110000q11001100r10101010p00001111(q r)11101110p(q r)000011105. Prove or disprove that the following 2 expressions are equivalent. Use either therelated laws for your proof, or complete the two truth tables:o (A + C)(AD + AD) + AC + Co A+C(A + C)(AD + AD) + AC + C(AD + AD) = ATherefore:= (A+C)A+ AC +C= AA+ AC + AC +C= A+ AC +C= A+C6. The following is a message coded in ASCII using one byte per character and thenrepresented in hexadecimal notation. What is the message?o 4469736372657465204D617468656D617469637320697320434F4F4C21Each letter in binary form takes 8 bits (1 byte). There is need to break the givenBOOLEAN ALGEBRA4hexadecimal code in parts of 2 characters then use the ASCII table to obtain thecoinciding characters.Hexadecimal 44 69 73 63 72 65 74 65204D 61 74 ...
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