diff options
Diffstat (limited to '3860/CH2')
48 files changed, 598 insertions, 0 deletions
diff --git a/3860/CH2/EX2.1/Ex2_1.sce b/3860/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..70b1a8303 --- /dev/null +++ b/3860/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,19 @@ +//Example 2.1: Develop truth table for a system with three inputs a,b and c and four outputs w,x,y and z
+clc // Clears the console
+disp("Develop truth table for a system with three inputs a,b and c and four outputs w,x,y and z")
+disp("Given conditions")
+disp("a = 0: odd a = 1: even")
+disp("b = 0: prime b = 1: not prime")
+disp("c = 0: less than 8 c = 1: greater than or equal to 8")
+disp("some input may never occur; the ouput is never all 0")
+disp("Inputs | Outputs")
+disp("A B C | W X Y Z")
+disp("0 0 0 | 0 1 1 1")
+disp("0 0 1 | 1 1 0 1")
+disp("0 1 0 | X X X X")
+disp("0 1 1 | 1 1 1 1")
+disp("1 0 0 | 0 0 1 0")
+disp("1 0 1 | X X X X")
+disp("1 1 0 | 0 1 1 0")
+disp("1 1 1 | 1 1 1 0")
+disp("The above table satisfies the given conditions.")
diff --git a/3860/CH2/EX2.1/Ex2_1.txt b/3860/CH2/EX2.1/Ex2_1.txt new file mode 100644 index 000000000..71aa5bebc --- /dev/null +++ b/3860/CH2/EX2.1/Ex2_1.txt @@ -0,0 +1,34 @@ +
+ Develop truth table for a system with three inputs a,b and c and four outputs w,x,y and z
+
+ Given conditions
+
+ a = 0: odd a = 1: even
+
+ b = 0: prime b = 1: not prime
+
+ c = 0: less than 8 c = 1: greater than or equal to 8
+
+ some input may never occur; the ouput is never all 0
+
+ Inputs | Outputs
+
+ A B C | W X Y Z
+
+ 0 0 0 | 0 1 1 1
+
+ 0 0 1 | 1 1 0 1
+
+ 0 1 0 | X X X X
+
+ 0 1 1 | 1 1 1 1
+
+ 1 0 0 | 0 0 1 0
+
+ 1 0 1 | X X X X
+
+ 1 1 0 | 0 1 1 0
+
+ 1 1 1 | 1 1 1 0
+
+ The above table satisfies the given conditions.
\ No newline at end of file diff --git a/3860/CH2/EX2.11/Ex2_11.sce b/3860/CH2/EX2.11/Ex2_11.sce new file mode 100644 index 000000000..17d2bde3b --- /dev/null +++ b/3860/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,9 @@ +//Example 2.11: Finding full adder expressions
+clc // Clears the console
+disp('For the full adder C is used as Cin ')
+disp('Cout = a''bc + ab''c + abc'' + abc')
+disp('s = a''b''c + a''bc'' + ab''c'' + abc')
+disp('The simplified expression of Cout is as given below')
+disp('Cout = bc + ac + ab')
+disp('s is already in minimum SOP form')
+
diff --git a/3860/CH2/EX2.11/Ex2_11.txt b/3860/CH2/EX2.11/Ex2_11.txt new file mode 100644 index 000000000..6727d6c01 --- /dev/null +++ b/3860/CH2/EX2.11/Ex2_11.txt @@ -0,0 +1,11 @@ + For the full adder C is used as Cin
+
+ Cout = a'bc + ab'c + abc' + abc
+
+ s = a'b'c + a'bc' + ab'c' + abc
+
+ The simplified expression of Cout is as given below
+
+ Cout = bc + ac + ab
+
+ s is already in minimum SOP form
\ No newline at end of file diff --git a/3860/CH2/EX2.15/Ex2_15.sce b/3860/CH2/EX2.15/Ex2_15.sce new file mode 100644 index 000000000..3538be05a --- /dev/null +++ b/3860/CH2/EX2.15/Ex2_15.sce @@ -0,0 +1,5 @@ +//Example 2.15: Reduce expression using Boolean laws
+clc // Clears the console
+disp('xyz + x''y + x''y'' = xyz + x''')
+disp(' = x'' + yz ')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.15/Ex2_15.txt b/3860/CH2/EX2.15/Ex2_15.txt new file mode 100644 index 000000000..8a9d3868e --- /dev/null +++ b/3860/CH2/EX2.15/Ex2_15.txt @@ -0,0 +1,4 @@ +
+ xyz + x'y + x'y' = xyz + x'
+
+ = x' + yz
\ No newline at end of file diff --git a/3860/CH2/EX2.16/Ex2_16.sce b/3860/CH2/EX2.16/Ex2_16.sce new file mode 100644 index 000000000..d3531235d --- /dev/null +++ b/3860/CH2/EX2.16/Ex2_16.sce @@ -0,0 +1,12 @@ +//Example 2.16: Reduce expression using Boolean laws
+clc // Clears the console
+disp('wx + wxy + w''yz + w''y''z + w''xyz''')
+disp(' = (wx + wxy) + (w''yz + w''y''z'') + w''xyz''')
+disp(' = wx + w''z + w''xyz''')
+disp(' = wx + w''(z + xyz'')')
+disp(' = wx + w''(z + xy)')
+disp(' = wx + w''z + w''xy)')
+disp(' =w''z + x( w + w''y)')
+disp(' =w''z + x( w + y)')
+disp(' =w''z + wx + xy')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.16/Ex2_16.txt b/3860/CH2/EX2.16/Ex2_16.txt new file mode 100644 index 000000000..4a0019680 --- /dev/null +++ b/3860/CH2/EX2.16/Ex2_16.txt @@ -0,0 +1,18 @@ +
+ wx + wxy + w'yz + w'y'z + w'xyz'
+
+ = (wx + wxy) + (w'yz + w'y'z') + w'xyz'
+
+ = wx + w'z + w'xyz'
+
+ = wx + w'(z + xyz')
+
+ = wx + w'(z + xy)
+
+ = wx + w'z + w'xy)
+
+ =w'z + x( w + w'y)
+
+ =w'z + x( w + y)
+
+ =w'z + wx + xy
\ No newline at end of file diff --git a/3860/CH2/EX2.17/Ex2_17.sce b/3860/CH2/EX2.17/Ex2_17.sce new file mode 100644 index 000000000..0e394e477 --- /dev/null +++ b/3860/CH2/EX2.17/Ex2_17.sce @@ -0,0 +1,8 @@ +//Example 2.17: Reduce expression using Boolean laws
+clc // Clears the console
+disp('(x + y)(x + y +z'') + y''')
+disp('=(x + y) + y''')
+disp('= x + (y + y'')')
+disp('= x + 1')
+disp('= 1')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.17/Ex2_17.txt b/3860/CH2/EX2.17/Ex2_17.txt new file mode 100644 index 000000000..539e97041 --- /dev/null +++ b/3860/CH2/EX2.17/Ex2_17.txt @@ -0,0 +1,10 @@ +
+ (x + y)(x + y +z') + y'
+
+ =(x + y) + y'
+
+ = x + (y + y')
+
+ = x + 1
+
+ = 1
\ No newline at end of file diff --git a/3860/CH2/EX2.18/Ex2_18.sce b/3860/CH2/EX2.18/Ex2_18.sce new file mode 100644 index 000000000..f26b41e4e --- /dev/null +++ b/3860/CH2/EX2.18/Ex2_18.sce @@ -0,0 +1,5 @@ +//Example 2.18: Reduce expression using Boolean laws
+clc // Clears the console
+disp('(a + b'' + c)(a + c'')(a'' + b''+ c)( a + c + d)')
+disp('=(b'' + c)(a + c'')( a + d'')')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.18/Ex2_18.txt b/3860/CH2/EX2.18/Ex2_18.txt new file mode 100644 index 000000000..9e42e80a9 --- /dev/null +++ b/3860/CH2/EX2.18/Ex2_18.txt @@ -0,0 +1,4 @@ +
+ (a + b' + c)(a + c')(a' + b'+ c)( a + c + d)
+
+ =(b' + c)(a + c')( a + d')
diff --git a/3860/CH2/EX2.2/Ex2_2.sce b/3860/CH2/EX2.2/Ex2_2.sce new file mode 100644 index 000000000..6abce8702 --- /dev/null +++ b/3860/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,38 @@ +//Example 2.2: Truth table based on three functions.
+clc // Clears the console
+disp("Truth Table")
+disp("f = y''z'' + x''y + x''yz''")
+disp("g = xy'' + x''z'' + x''y")
+disp("h = (x'' + y'')(x + y + z''")
+disp('****************************************')
+disp("x y z | y''z'' x''y x''yz'' | f")
+disp("0 0 0 | 1 0 0 | 1")
+disp("0 0 1 | 0 0 0 | 0")
+disp("0 1 0 | 0 1 1 | 1")
+disp("0 1 1 | 0 1 0 | 1")
+disp("1 0 0 | 1 0 0 | 1")
+disp("1 0 1 | 0 0 0 | 0")
+disp("1 1 0 | 0 0 0 | 0")
+disp("1 1 1 | 0 0 0 | 0")
+disp('****************************************')
+disp("x y z | xy'' x''z'' x''y | g")
+disp("0 0 0 | 0 1 0 | 1")
+disp("0 0 1 | 0 0 0 | 0")
+disp("0 1 0 | 0 1 1 | 1")
+disp("0 1 1 | 0 0 1 | 1")
+disp("1 0 0 | 1 0 0 | 1")
+disp("1 0 1 | 1 0 0 | 1")
+disp("1 1 0 | 0 0 0 | 0")
+disp("1 1 1 | 0 0 0 | 0")
+disp('****************************************')
+disp("x y z | x''+ y'' x + y + z'' | h")
+disp("0 0 0 | 1 1 | 1")
+disp("0 0 1 | 1 0 | 0")
+disp("0 1 0 | 1 1 | 1")
+disp("0 1 1 | 1 1 | 1")
+disp("1 0 0 | 1 1 | 1")
+disp("1 0 1 | 1 1 | 1")
+disp("1 1 0 | 0 1 | 0")
+disp("1 1 1 | 0 1 | 0")
+disp('****************************************')
+disp("The functions g and h are identical.")
diff --git a/3860/CH2/EX2.2/Ex2_2.txt b/3860/CH2/EX2.2/Ex2_2.txt new file mode 100644 index 000000000..114867951 --- /dev/null +++ b/3860/CH2/EX2.2/Ex2_2.txt @@ -0,0 +1,72 @@ +
+ Truth Table
+
+ f = y'z' + x'y + x'yz'
+
+ g = xy' + x'z' + x'y
+
+ h = (x' + y')(x + y + z'
+
+ ****************************************
+
+ x y z | y'z' x'y x'yz' | f
+
+ 0 0 0 | 1 0 0 | 1
+
+ 0 0 1 | 0 0 0 | 0
+
+ 0 1 0 | 0 1 1 | 1
+
+ 0 1 1 | 0 1 0 | 1
+
+ 1 0 0 | 1 0 0 | 1
+
+ 1 0 1 | 0 0 0 | 0
+
+ 1 1 0 | 0 0 0 | 0
+
+ 1 1 1 | 0 0 0 | 0
+
+ ****************************************
+
+ x y z | xy' x'z' x'y | g
+
+ 0 0 0 | 0 1 0 | 1
+
+ 0 0 1 | 0 0 0 | 0
+
+ 0 1 0 | 0 1 1 | 1
+
+ 0 1 1 | 0 0 1 | 1
+
+ 1 0 0 | 1 0 0 | 1
+
+ 1 0 1 | 1 0 0 | 1
+
+ 1 1 0 | 0 0 0 | 0
+
+ 1 1 1 | 0 0 0 | 0
+
+ ****************************************
+
+ x y z | x'+ y' x + y + z' | h
+
+ 0 0 0 | 1 1 | 1
+
+ 0 0 1 | 1 0 | 0
+
+ 0 1 0 | 1 1 | 1
+
+ 0 1 1 | 1 1 | 1
+
+ 1 0 0 | 1 1 | 1
+
+ 1 0 1 | 1 1 | 1
+
+ 1 1 0 | 0 1 | 0
+
+ 1 1 1 | 0 1 | 0
+
+ ****************************************
+
+ The functions g and h are identical.
diff --git a/3860/CH2/EX2.20/Ex2_20.sce b/3860/CH2/EX2.20/Ex2_20.sce new file mode 100644 index 000000000..6419ebb54 --- /dev/null +++ b/3860/CH2/EX2.20/Ex2_20.sce @@ -0,0 +1,6 @@ +//Example 2.20: Reduce expression using Boolean laws ( Consensus Theorem)
+clc // Clears the console
+disp('f = a''b''c'' + a''bc'' + a''bc + ab''c''')
+disp('f1 = a''c'' + a''b + b''c''')
+disp('f2 = b''c'' + a''b reduced using consensus theorem') //term a'c' is removed as it is the consensus of other two terms.
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.20/Ex2_20.txt b/3860/CH2/EX2.20/Ex2_20.txt new file mode 100644 index 000000000..59248e28c --- /dev/null +++ b/3860/CH2/EX2.20/Ex2_20.txt @@ -0,0 +1,6 @@ +
+ f = a'b'c' + a'bc' + a'bc + ab'c'
+
+ f1 = a'c' + a'b + b'c'
+
+ f2 = b'c' + a'b reduced using consensus theorem
\ No newline at end of file diff --git a/3860/CH2/EX2.21/Ex2_21.sce b/3860/CH2/EX2.21/Ex2_21.sce new file mode 100644 index 000000000..a68c11acc --- /dev/null +++ b/3860/CH2/EX2.21/Ex2_21.sce @@ -0,0 +1,7 @@ +//Example 2.21: Reduce expression using Boolean laws ( Consensus Theorem)
+clc // Clears the console
+disp('g = bc'' + abd + acd ')
+disp('the only consensus term defined is bc''$ acd = abd')
+disp('g = bc'' + acd ')//removing consensus term
+
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.21/Ex2_21.txt b/3860/CH2/EX2.21/Ex2_21.txt new file mode 100644 index 000000000..3628d2d4b --- /dev/null +++ b/3860/CH2/EX2.21/Ex2_21.txt @@ -0,0 +1,6 @@ +
+ g = bc' + abd + acd
+
+ the only consensus term defined is bc'$ acd = abd
+
+ g = bc' + acd
diff --git a/3860/CH2/EX2.22/Ex2_22.sce b/3860/CH2/EX2.22/Ex2_22.sce new file mode 100644 index 000000000..1be2190ee --- /dev/null +++ b/3860/CH2/EX2.22/Ex2_22.sce @@ -0,0 +1,8 @@ +//Example 2.22: Reduce expression using Boolean laws ( Consensus Theorem)
+clc // Clears the console
+disp('f = c''d''+ ac'' + ad + bd'' + ab ')
+disp('Two terms can be reduced using consensus twice')
+disp('c''d'' $ ad = ac'' and ad $ bd'' = ab')
+disp('Thus we can remove ac'' and ab leaving')
+disp('f = c''d''+ ad + bd'' ')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.22/Ex2_22.txt b/3860/CH2/EX2.22/Ex2_22.txt new file mode 100644 index 000000000..fe62e006e --- /dev/null +++ b/3860/CH2/EX2.22/Ex2_22.txt @@ -0,0 +1,10 @@ +
+ f = c'd'+ ac' + ad + bd' + ab
+
+ Two terms can be reduced using consensus twice
+
+ c'd' $ ad = ac' and ad $ bd' = ab
+
+ Thus we can remove ac' and ab leaving
+
+ f = c'd'+ ad + bd'
diff --git a/3860/CH2/EX2.23/Ex2_23.sce b/3860/CH2/EX2.23/Ex2_23.sce new file mode 100644 index 000000000..5540da369 --- /dev/null +++ b/3860/CH2/EX2.23/Ex2_23.sce @@ -0,0 +1,7 @@ +//Example 2.23: Reduce expression using Boolean laws
+clc // Clears the console
+disp('A''BCD + A''BC''D + B''EF + CDE''G + A''DEF + A''B''EF')
+disp('= A''BD + B''EF + CDE''G + A''DEF')
+disp('But A''BD $ B''EF = A''DEF and this reduces to ')
+disp('= A''BD + B''EF + CDE''G')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.23/Ex2_23.txt b/3860/CH2/EX2.23/Ex2_23.txt new file mode 100644 index 000000000..d170e37ef --- /dev/null +++ b/3860/CH2/EX2.23/Ex2_23.txt @@ -0,0 +1,8 @@ +
+ A'BCD + A'BC'D + B'EF + CDE'G + A'DEF + A'B'EF
+
+ = A'BD + B'EF + CDE'G + A'DEF
+
+ But A'BD $ B'EF = A'DEF and this reduces to
+
+ = A'BD + B'EF + CDE'G
\ No newline at end of file diff --git a/3860/CH2/EX2.24/Ex2_24.sce b/3860/CH2/EX2.24/Ex2_24.sce new file mode 100644 index 000000000..434b63909 --- /dev/null +++ b/3860/CH2/EX2.24/Ex2_24.sce @@ -0,0 +1,8 @@ +//Example 2.24: Reduce expression using Boolean laws
+clc // Clears the console
+disp('w''xy + wz + xz + w''y''z + w''xy'' + wx''z')
+disp('= wz + w''x + xz +w''y''z')
+disp('= wz + w''x + w''y''z since wz $ w''x = xz')
+disp('But wz +w''y''z = z(w + w''y'') = z(w + y'')')
+disp('= wz + w''x + y''z ')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.24/Ex2_24.txt b/3860/CH2/EX2.24/Ex2_24.txt new file mode 100644 index 000000000..e29704804 --- /dev/null +++ b/3860/CH2/EX2.24/Ex2_24.txt @@ -0,0 +1,10 @@ +
+ w'xy + wz + xz + w'y'z + w'xy' + wx'z
+
+ = wz + w'x + xz +w'y'z
+
+ = wz + w'x + w'y'z since wz $ w'x = xz
+
+ But wz +w'y'z = z(w + w'y') = z(w + y')
+
+ = wz + w'x + y'z
\ No newline at end of file diff --git a/3860/CH2/EX2.25/Ex2_25.sce b/3860/CH2/EX2.25/Ex2_25.sce new file mode 100644 index 000000000..7d0f0bcbe --- /dev/null +++ b/3860/CH2/EX2.25/Ex2_25.sce @@ -0,0 +1,8 @@ +//Example 2.25: Manipulation of algebric functions.
+clc // Clears the console
+disp('f = bc + ac + ab ')
+disp('f = bca + bca'' + ac + ab ')// converting into disjunctive normal form.
+disp('f = bca + bca'' + acb + acb'' + abc + abc'' ')
+disp('f = abc + a''bc + abc + ab''c + abc + abc'' ')// arranging into alphabetical order
+disp('f = a''bc + ab''c + abc'' + abc ') //removing duplicate terms.
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.25/Ex2_25.txt b/3860/CH2/EX2.25/Ex2_25.txt new file mode 100644 index 000000000..481f671ef --- /dev/null +++ b/3860/CH2/EX2.25/Ex2_25.txt @@ -0,0 +1,10 @@ +
+ f = bc + ac + ab
+
+ f = bca + bca' + ac + ab
+
+ f = bca + bca' + acb + acb' + abc + abc'
+
+ f = abc + a'bc + abc + ab'c + abc + abc'
+
+ f = a'bc + ab'c + abc' + abc
\ No newline at end of file diff --git a/3860/CH2/EX2.26/Ex2_26.sce b/3860/CH2/EX2.26/Ex2_26.sce new file mode 100644 index 000000000..2a95f1284 --- /dev/null +++ b/3860/CH2/EX2.26/Ex2_26.sce @@ -0,0 +1,6 @@ +//Example 2.26: Conversion of Boolean expression into minterm expression
+clc // Clears the console
+disp('g = x'' + xyz')
+disp(' = x''yz + x''yz'' + x''y''z + x''y''z'' + xyz')
+disp('g(x,y,z) = summation of minterms( 3,2,1,0,7) = summation of minterms ( 0,1,2,3,7)')//Since minterm numbers are usually written in numeric order.
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.26/Ex2_26.txt b/3860/CH2/EX2.26/Ex2_26.txt new file mode 100644 index 000000000..3bcb86c96 --- /dev/null +++ b/3860/CH2/EX2.26/Ex2_26.txt @@ -0,0 +1,6 @@ +
+ g = x' + xyz
+
+ = x'yz + x'yz' + x'y'z + x'y'z' + xyz
+
+ g(x,y,z) = summation of minterms( 3,2,1,0,7) = summation of minterms ( 0,1,2,3,7)
\ No newline at end of file diff --git a/3860/CH2/EX2.27/Ex2_27.sce b/3860/CH2/EX2.27/Ex2_27.sce new file mode 100644 index 000000000..c894d3af3 --- /dev/null +++ b/3860/CH2/EX2.27/Ex2_27.sce @@ -0,0 +1,6 @@ +//Example 2.27: Manipulation of algebric functions into POS form.
+clc // Clears the console
+disp('f = (A + B + C) ( A'' + B'')')
+disp('f = (A + B + C) ( A'' + B'' + C) ( A'' + B'' + C'')')// converting into disjunctive normal form.
+disp(' The POS form of given expression is displayed')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.27/Ex2_27.txt b/3860/CH2/EX2.27/Ex2_27.txt new file mode 100644 index 000000000..fa3d2890a --- /dev/null +++ b/3860/CH2/EX2.27/Ex2_27.txt @@ -0,0 +1,6 @@ +
+ f = (A + B + C) ( A' + B')
+
+ f = (A + B + C) ( A' + B' + C) ( A' + B' + C')
+
+ The POS form of given expression is displayed
\ No newline at end of file diff --git a/3860/CH2/EX2.28/Ex2_28.sce b/3860/CH2/EX2.28/Ex2_28.sce new file mode 100644 index 000000000..9cbaa3602 --- /dev/null +++ b/3860/CH2/EX2.28/Ex2_28.sce @@ -0,0 +1,8 @@ +//Example 2.28: Manipulation POS expression into SOP Expression.
+clc // Clears the console
+disp('f = (A + B + C) ( A'' + B'') = AB'' + A''( B + C) = AB'' + A''B + A''C')
+disp('f = AA'' + AB'' + BA'' + BB'' + CA'' + CB''')// converting into disjunctive normal form.
+disp('f = AB'' + A''B + A''C + B''C')
+disp(' The SOP form of given expression is displayed')
+disp(' The term B''C can then be removed because it is the consensus of AB'' and A''C')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.28/Ex2_28.txt b/3860/CH2/EX2.28/Ex2_28.txt new file mode 100644 index 000000000..a7378e954 --- /dev/null +++ b/3860/CH2/EX2.28/Ex2_28.txt @@ -0,0 +1,10 @@ +
+ f = (A + B + C) ( A' + B') = AB' + A'( B + C) = AB' + A'B + A'C
+
+ f = AA' + AB' + BA' + BB' + CA' + CB'
+
+ f = AB' + A'B + A'C + B'C
+
+ The SOP form of given expression is displayed
+
+ The term B'C can then be removed because it is the consensus of AB' and A'C
\ No newline at end of file diff --git a/3860/CH2/EX2.29/Ex2_29.sce b/3860/CH2/EX2.29/Ex2_29.sce new file mode 100644 index 000000000..b1d6c3351 --- /dev/null +++ b/3860/CH2/EX2.29/Ex2_29.sce @@ -0,0 +1,8 @@ +//Example 2.29: Manipulation POS expression into SOP Expression.
+clc // Clears the console
+disp('(A + B'' + C) ( A + B + D) (A'' + C'' + D'')')
+disp(' = [A + (B'' + C)(B + D)](A'' + C'' + D''')
+disp(' = (A + B''D + BC)(A'' + C'' + D'')')
+disp(' = A ( C''+ D'') + A''(B''D + BC )')
+disp(' = AC'' + AD'' + A''B''D + A''BC')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.29/Ex2_29.txt b/3860/CH2/EX2.29/Ex2_29.txt new file mode 100644 index 000000000..dbfa6d9bc --- /dev/null +++ b/3860/CH2/EX2.29/Ex2_29.txt @@ -0,0 +1,10 @@ +
+ (A + B' + C) ( A + B + D) (A' + C' + D')
+
+ = [A + (B' + C)(B + D)](A' + C' + D'
+
+ = (A + B'D + BC)(A' + C' + D')
+
+ = A ( C'+ D') + A'(B'D + BC )
+
+ = AC' + AD' + A'B'D + A'BC
diff --git a/3860/CH2/EX2.3/EX2_3.sce b/3860/CH2/EX2.3/EX2_3.sce new file mode 100644 index 000000000..f2196b787 --- /dev/null +++ b/3860/CH2/EX2.3/EX2_3.sce @@ -0,0 +1,10 @@ +//Example 2.3: Reduce a given expression
+clc; //clears the console
+clear; //clears all existing variables
+//the given expression is as follows//
+disp(' Given Expression- A''B''C''+ A''BC''+ A''BC + AB''C''')
+disp('A''C''+ A''BC + AB''C''')
+disp('A''C''+ A''B + AB''C''')
+disp('A''C''+ A''B + B''C''')
+disp('The reduced expression is = ')
+disp('B''C''+ A''B') //final reduced expression is displayed//
diff --git a/3860/CH2/EX2.3/Ex2_3.txt b/3860/CH2/EX2.3/Ex2_3.txt new file mode 100644 index 000000000..ad6051b6a --- /dev/null +++ b/3860/CH2/EX2.3/Ex2_3.txt @@ -0,0 +1,12 @@ +
+ Given Expression- A'B'C'+ A'BC'+ A'BC + AB'C'
+
+ A'C'+ A'BC + AB'C'
+
+ A'C'+ A'B + AB'C'
+
+ A'C'+ A'B + B'C'
+
+ The reduced expression is =
+
+ B'C'+ A'B
diff --git a/3860/CH2/EX2.30/Ex2_30.sce b/3860/CH2/EX2.30/Ex2_30.sce new file mode 100644 index 000000000..6980820ee --- /dev/null +++ b/3860/CH2/EX2.30/Ex2_30.sce @@ -0,0 +1,8 @@ +//Example 2.30: Convert expression into POS Form
+clc // Clears the console
+disp('wxy'' + xyz + w''x''z''')
+disp('= x(wy'' + yz) + w''x''z''')
+disp('= x(y'' + z)(y + w) + w''x''z''')
+disp('= (x + w''z'')[x'' + (y'' + z )(y + w)]')
+disp('= (x + w'')(x + z'')(x'' + y'' + z )(x'' + y + w)]')
+//the reduced expression is displayed.
diff --git a/3860/CH2/EX2.30/Ex2_30.txt b/3860/CH2/EX2.30/Ex2_30.txt new file mode 100644 index 000000000..bed251468 --- /dev/null +++ b/3860/CH2/EX2.30/Ex2_30.txt @@ -0,0 +1,10 @@ +
+ wxy' + xyz + w'x'z'
+
+ = x(wy' + yz) + w'x'z'
+
+ = x(y' + z)(y + w) + w'x'z'
+
+ = (x + w'z')[x' + (y' + z )(y + w)]
+
+ = (x + w')(x + z')(x' + y' + z )(x' + y + w)]
\ No newline at end of file diff --git a/3860/CH2/EX2.5/EX2_5.sce b/3860/CH2/EX2.5/EX2_5.sce new file mode 100644 index 000000000..57add8e50 --- /dev/null +++ b/3860/CH2/EX2.5/EX2_5.sce @@ -0,0 +1,8 @@ +//Example 2.5: Use of Demorgans Theorem.to find complement of a given function.
+clc; //clears the console
+clear; //clears all existing variables
+disp('The given expression is as follows')
+disp('f = wx''y + xy'' + wxz')
+disp('f'' = (wx''y + xy'' + wxz)''')
+disp('f'' = (wx''y)''(xy'')''(wxz)''')
+disp('f'' = (w''+ x + y'')(x'' + y)(w'' + x''+ z'')')
diff --git a/3860/CH2/EX2.5/Ex2_5.txt b/3860/CH2/EX2.5/Ex2_5.txt new file mode 100644 index 000000000..b7ac1e29b --- /dev/null +++ b/3860/CH2/EX2.5/Ex2_5.txt @@ -0,0 +1,9 @@ + The given expression is as follows
+
+ f = wx'y + xy' + wxz
+
+ f' = (wx'y + xy' + wxz)'
+
+ f' = (wx'y)'(xy')'(wxz)'
+
+ f' = (w'+ x + y')(x' + y)(w' + x'+ z')
\ No newline at end of file diff --git a/3860/CH2/EX2.6/EX2_6.sce b/3860/CH2/EX2.6/EX2_6.sce new file mode 100644 index 000000000..810a106b8 --- /dev/null +++ b/3860/CH2/EX2.6/EX2_6.sce @@ -0,0 +1,11 @@ +//Example 2.6: Use of Demorgans Theorem.to find complement of a given function.
+clc; //clears the console
+clear; //clears all existing variables
+disp('The given expression is as follows')
+disp('f = ab''(c + d''e) + a''bc'')')
+disp('Finding complement using Demorgan''s Theorem')
+disp('f'' = [ab''(c + d''e) + a''bc'']''')
+disp('f'' = [ab''(c + d''e)]'' [a''bc'']''')
+disp('f'' = [a'' + b + (c + d''e)''][a + b'' + c]')
+disp('f'' = [a'' + b + c''(d''e)''][a + b'' + c]')
+disp('f'' = [a'' + b + c''(d + e'')][a + b'' + c]')
diff --git a/3860/CH2/EX2.6/Ex2_6.txt b/3860/CH2/EX2.6/Ex2_6.txt new file mode 100644 index 000000000..bf14f6357 --- /dev/null +++ b/3860/CH2/EX2.6/Ex2_6.txt @@ -0,0 +1,16 @@ +
+ The given expression is as follows
+
+ f = ab'(c + d'e) + a'bc')
+
+ Finding complement using Demorgan's Theorem
+
+ f' = [ab'(c + d'e) + a'bc']'
+
+ f' = [ab'(c + d'e)]' [a'bc']'
+
+ f' = [a' + b + (c + d'e)'][a + b' + c]
+
+ f' = [a' + b + c'(d'e)'][a + b' + c]
+
+ f' = [a' + b + c'(d + e')][a + b' + c]
\ No newline at end of file diff --git a/3860/CH2/EX2.7/Ex2_7.sce b/3860/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..703161ec9 --- /dev/null +++ b/3860/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,20 @@ +//Example 2.7: Finding POS form from given truth table.
+clc // Clears the console
+disp('Given truth table')
+disp('****************************************')
+disp("A B C | f f''")
+disp("0 0 0 | 1 1")
+disp("0 0 1 | 0 0")
+disp("0 1 0 | 1 0")
+disp("0 1 1 | 1 0")
+disp("1 0 0 | 1 0")
+disp("1 0 1 | 0 0")
+disp("1 1 0 | 0 1")
+disp("1 1 1 | 0 1")
+disp('f(A,B,C) = summation(1,2,3,4,5)')
+disp('The complement of function is as given below')
+disp('f''(A,B,C) = summation(0,6,7)')
+disp(' = A''B''C'' + ABC'' + ABC ')
+disp(' = A''B''C'' + AB')
+disp('f = (A + B + C)(A'' + B''')
+disp('This is the reduced POS expression')
diff --git a/3860/CH2/EX2.7/Ex2_7.txt b/3860/CH2/EX2.7/Ex2_7.txt new file mode 100644 index 000000000..4f835c667 --- /dev/null +++ b/3860/CH2/EX2.7/Ex2_7.txt @@ -0,0 +1,36 @@ +
+ Given truth table
+
+ ****************************************
+
+ A B C | f f'
+
+ 0 0 0 | 1 1
+
+ 0 0 1 | 0 0
+
+ 0 1 0 | 1 0
+
+ 0 1 1 | 1 0
+
+ 1 0 0 | 1 0
+
+ 1 0 1 | 0 0
+
+ 1 1 0 | 0 1
+
+ 1 1 1 | 0 1
+
+ f(A,B,C) = summation(1,2,3,4,5)
+
+ The complement of function is as given below
+
+ f'(A,B,C) = summation(0,6,7)
+
+ = A'B'C' + ABC' + ABC
+
+ = A'B'C' + AB
+
+ f = (A + B + C)(A' + B'
+
+ This is the reduced POS expression
\ No newline at end of file diff --git a/3860/CH2/EX2.8/Ex2_8.sce b/3860/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..2615336b3 --- /dev/null +++ b/3860/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,13 @@ +//Example 2.8: Representation of truth table from minterm expression
+clc // Clears the console
+disp("f(a,b,c) = Summation minterms (1,2,5) + Summation dont cares (0,3)")
+disp('implies that minterms 1,2 and 5 are included in the function and that 0 and 3 are dont cares, that is the truth table is as follows:')
+disp("a b c | f")
+disp("0 0 0 | x")
+disp("0 0 1 | 1")
+disp("0 1 0 | 1")
+disp("0 1 1 | x")
+disp("1 0 0 | 0")
+disp("1 0 1 | 1")
+disp("1 1 0 | 0")
+disp("1 1 1 | 0")
diff --git a/3860/CH2/EX2.8/Ex2_8.txt b/3860/CH2/EX2.8/Ex2_8.txt new file mode 100644 index 000000000..8d138f2ef --- /dev/null +++ b/3860/CH2/EX2.8/Ex2_8.txt @@ -0,0 +1,22 @@ +
+ f(a,b,c) = Summation minterms (1,2,5) + Summation dont cares (0,3)
+
+ implies that minterms 1,2 and 5 are included in the function and that 0 and 3 are dont cares, that is the truth table is as follows:
+
+ a b c | f
+
+ 0 0 0 | x
+
+ 0 0 1 | 1
+
+ 0 1 0 | 1
+
+ 0 1 1 | x
+
+ 1 0 0 | 0
+
+ 1 0 1 | 1
+
+ 1 1 0 | 0
+
+ 1 1 1 | 0
\ No newline at end of file diff --git a/3860/CH2/EX2.9/Ex2_9.sce b/3860/CH2/EX2.9/Ex2_9.sce new file mode 100644 index 000000000..75d02db23 --- /dev/null +++ b/3860/CH2/EX2.9/Ex2_9.sce @@ -0,0 +1,8 @@ +//Example 2.9: Finding reduced boolean expression using Boolean laws
+clc // Clears the console
+disp('Z2 = A''BCD + AB''CD + ABC''D + ABCD'' + ABCD')
+disp('the last terms ABCD can be combined with each of the others. Thus, if we make four copies of it and then utilize for times we obtain')
+disp('Z2 = BCD + ACD + ABD + ABC')
+disp('No further simplification is possible; this is minimum SOP form')
+disp('Z1 = A''BCD + AB''CD + ABC''D + ABCD'' ')
+disp('In case of Z1 no simplification is possible it has 16 literals whereas expression for Z2 only has 12 literals.')
diff --git a/3860/CH2/EX2.9/Ex2_9.txt b/3860/CH2/EX2.9/Ex2_9.txt new file mode 100644 index 000000000..66f2c0d78 --- /dev/null +++ b/3860/CH2/EX2.9/Ex2_9.txt @@ -0,0 +1,12 @@ +
+ Z2 = A'BCD + AB'CD + ABC'D + ABCD' + ABCD
+
+ the last terms ABCD can be combined with each of the others. Thus, if we make four copies of it and then utilize for times we obtain
+
+ Z2 = BCD + ACD + ABD + ABC
+
+ No further simplification is possible; this is minimum SOP form
+
+ Z1 = A'BCD + AB'CD + ABC'D + ABCD'
+
+ In case of Z1 no simplification is possible it has 16 literals whereas expression for Z2 only has 12 literals.
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