I need help with some Boolean algebra questions, just 2.5a, 2.6b and 2.8a any he
ID: 3742182 • Letter: I
Question
I need help with some Boolean algebra questions, just 2.5a, 2.6b and 2.8a
any help would be appreciated
A- 0o) 2.5 Multiply out and simplify to obtain a sum of products (a) (A + BC+BD +B(ACD E (b) (A+B+CA+C + DYB +D') 2.6 Factor each of the following expressions to obtain a product of sums: (a) AB+ CD (c) ABC+ EF +DEF (d) XYZ+ WZ+ xQZ (e) ACD, + C'D' + A"C (f) A + BC + DE (The answer to (1) should be the product of four terms,each a sum of three variables.) 2.7 Draw a circuit that uses only one AND gate and one OR gate to realize each of the (a) (A+ B +C+DKA+B+C+EMA +B+C+F) 2.8 Simplify the following expressions to a minimum sum of products (a) I(AB), + C.DI, (b) [A + B(C' + D)1. (c) ((A + ')C),(A + BXC +AY 2.9 Find F and G and simplify: Boolean Algebra 55Explanation / Answer
2.5A )
(A + B )(C + B)(D' + B)(ACD' + E)
=> (A + B )(C + B)(D' + B)(ACD' + E)
=> (AB + AC + BC + B )(D' + B)(ACD' + E)
=> (AC + B (A + 1 + 1 )(D' + B)(ACD' + E) [As we know 1 + A = 1]
=> (AC + B )(D' + B)(ACD' + E)
=> (AC + B )(D' + B)(ACD' + E)
=> (ACD' + ABC + BD' + B)(ACD' + E)
=> (ACD' + B ( AC + D' + 1))(ACD' + E)
=> (ACD' + B )(ACD' + E) [As we know 1 + A = 1]
=> ACD' + ACD'E + ABCD' + BE
=> ACD' ( 1 + 'E + B ) + BE
=> ACD' + BE
2.6B) F = WX + WY'X + ZYX
F' = ( WX + WY'X + ZYX )'
=> ( WX )' ( WY'X ) ' ( ZYX )'
=> ( W' + X' ) ( W' + Y + X' ) + ( Z' + Y' + X' )
=> ( W' + W'Y + W'X' + W'X' + X' Y + X' ) + ( Z' + Y' + X' ) [Take X' common from we get]
=> ( W' + W'Y + X' ) + ( Z' + Y' + X' )
=> ( W' Z + W'Y + W'X' + W'YZ' + W'X'Y + X'Z' + X'Y' + X' )
=> ( W' Z + W'Y + W'YZ' + X' (W' +W'Y + Z' + Y' + 1 )
=> ( W' Z + W'Y + W'YZ' + X')
f''=> ( W' Z + W'Y + W'YZ' + X') '
=> ( W' Z)' ( W'Y ) ' (W'YZ') ' (X') '
=> (W + Z' ) (W + Y' ) (W + Y + Z) (X)
2.8 (A ) [( AB )' + CD ]'
=> [( AB ) (CD )' ]
=> AB [ C' + D' ]
=> ABC' + ABD'
Thanks, let me know if there is any concern.