diff options
Diffstat (limited to '2459/CH28')
26 files changed, 202 insertions, 0 deletions
diff --git a/2459/CH28/EX28.1/Ex28_1.PNG b/2459/CH28/EX28.1/Ex28_1.PNG Binary files differnew file mode 100644 index 000000000..51acc036f --- /dev/null +++ b/2459/CH28/EX28.1/Ex28_1.PNG diff --git a/2459/CH28/EX28.1/Ex28_1.sce b/2459/CH28/EX28.1/Ex28_1.sce new file mode 100644 index 000000000..7bbf45559 --- /dev/null +++ b/2459/CH28/EX28.1/Ex28_1.sce @@ -0,0 +1,6 @@ +//chapter28
+//example28.1
+//page590
+
+a= dec2bin (37)
+disp(a,'binary equivalent of decimal number 37 = ')
diff --git a/2459/CH28/EX28.10/Ex28_10.PNG b/2459/CH28/EX28.10/Ex28_10.PNG Binary files differnew file mode 100644 index 000000000..b38ab34a0 --- /dev/null +++ b/2459/CH28/EX28.10/Ex28_10.PNG diff --git a/2459/CH28/EX28.10/Ex28_10.sce b/2459/CH28/EX28.10/Ex28_10.sce new file mode 100644 index 000000000..c1384b904 --- /dev/null +++ b/2459/CH28/EX28.10/Ex28_10.sce @@ -0,0 +1,19 @@ +//chapter28
+//example28.10
+//page607
+
+printf("1) Y = A . B . C` + A . ( B . C )` \n")
+printf(" Y` = ( A . B . C` + A . ( B . C )` )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y` = ( A . B . C`)` . ( A . ( B . C)` )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y` = ( A` + B` + C ) . ( A` + B + C ) \n \n")
+printf("2) Y = A` . ( B .C` + B` . C ) \n")
+printf(" Y` = ( A` . ( B .C` + B` . C ) )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y` = A + ( B . C` + B` .C )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y` = A + ( B . C`)` . ( B` . C )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y` = A + ( B` + C ) . ( B + C`) \n")
+printf(" Y` = A + ( B . C )` + ( B . C ) \n")
diff --git a/2459/CH28/EX28.11/Ex28_11.PNG b/2459/CH28/EX28.11/Ex28_11.PNG Binary files differnew file mode 100644 index 000000000..1fa7348d8 --- /dev/null +++ b/2459/CH28/EX28.11/Ex28_11.PNG diff --git a/2459/CH28/EX28.11/Ex28_11.sce b/2459/CH28/EX28.11/Ex28_11.sce new file mode 100644 index 000000000..03ccc64a3 --- /dev/null +++ b/2459/CH28/EX28.11/Ex28_11.sce @@ -0,0 +1,37 @@ +//chapter28
+//example28.11
+//page608
+
+printf("1) Y = ( A + B + C ) . ( A + B ) \n")
+printf(" Y = A . A + A . B + B . A + B . B + C . A + C . B \n")
+printf(" Using A . A = A we get \n")
+printf(" Y = A + A . B + A . B + B + A . C + B . C \n")
+printf(" Using A . B + A . B = A . B we get \n")
+printf(" Y = A + A . B + B + A . C + B . C \n")
+printf(" Using A + A . B = A we get \n")
+printf(" Y = A + B + A . C + B . C \n")
+printf(" = A . ( 1 + C ) + B . ( 1 + C ) \n")
+printf(" Using 1 + C = 1 we get \n")
+printf(" Y = A . 1 + B . 1 \n")
+printf(" Y = A + B \n \n")
+
+printf("2) Y = A . B + A . B . C + A . B . C` \n")
+printf(" = A . B + A . B ( C + C` ) \n")
+printf(" Since C + C` = 1 we get \n")
+printf(" Y = A . B + A . B \n")
+printf(" = A . B \n \n")
+
+
+printf("3) Y = 1 + A . ( B . C` + B . C + B` . C`) + A . B` . C + A . C \n")
+printf(" Using 1 + A = 1 and 1 + A . ( B . C` + B . C + ( B . C )` ) = 1 we get \n")
+printf(" Y = 1 + A . B` . C + A . C \n")
+printf(" Y = 1 + A . C \n")
+printf(" Y = 1 \n \n")
+
+printf("4) Y = ( ( A + B` + C ) + ( B + C` ))` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y = ( A + B` + C )` . ( B + C` )` \n")
+printf(" By De Morgan theorem \n")
+printf(" Y = ( A` . B . C` ) . ( B` . C ) \n")
+printf(" Since B . B` = 0 and C . C` = 0 we get \n")
+printf(" Y = 0 \n")
diff --git a/2459/CH28/EX28.12/Ex28_12.PNG b/2459/CH28/EX28.12/Ex28_12.PNG Binary files differnew file mode 100644 index 000000000..3c2b1601c --- /dev/null +++ b/2459/CH28/EX28.12/Ex28_12.PNG diff --git a/2459/CH28/EX28.12/Ex28_12.sce b/2459/CH28/EX28.12/Ex28_12.sce new file mode 100644 index 000000000..be9de6438 --- /dev/null +++ b/2459/CH28/EX28.12/Ex28_12.sce @@ -0,0 +1,11 @@ +//chapter28
+//example28.12
+//page609
+
+printf(" Y = A . B` . D + A . B` . D` \n")
+printf(" Factor out A . B` by theorem 14 \n")
+printf(" Y = A . B` ( D + D` ) \n")
+printf(" But by theorem 3 D + D` = 1 \n")
+printf(" Y = A . B` . 1 \n")
+printf(" By theorem 2 \n")
+printf(" Y = A . B` \n")
diff --git a/2459/CH28/EX28.13/Ex28_13.PNG b/2459/CH28/EX28.13/Ex28_13.PNG Binary files differnew file mode 100644 index 000000000..56afb45c5 --- /dev/null +++ b/2459/CH28/EX28.13/Ex28_13.PNG diff --git a/2459/CH28/EX28.13/Ex28_13.sce b/2459/CH28/EX28.13/Ex28_13.sce new file mode 100644 index 000000000..1a835d6c6 --- /dev/null +++ b/2459/CH28/EX28.13/Ex28_13.sce @@ -0,0 +1,19 @@ +//chapter28
+//example28.13
+//page609
+
+printf(" Y = ( A` + B ) . ( A + B ) \n")
+printf(" By theorem 15 \n")
+printf(" Y = A` . A + A` . B + B . A + B . B \n")
+printf(" By theorem 4 and 6 \n")
+printf(" Y = 0 + A` . B + B . A + B \n")
+printf(" Y = A` . B + B . A + B \n")
+
+printf(" By theorem 14 \n")
+printf(" Y = B . ( A` + A + 1 ) \n")
+printf(" By theorem 7 \n")
+printf(" Y = B . ( A` + 1 ) \n")
+printf(" By theorem 7 \n")
+printf(" Y = B . 1 ) \n")
+printf(" By theorem 2 \n")
+printf(" Y = B \n")
diff --git a/2459/CH28/EX28.2/Ex28_2.PNG b/2459/CH28/EX28.2/Ex28_2.PNG Binary files differnew file mode 100644 index 000000000..f114f6d08 --- /dev/null +++ b/2459/CH28/EX28.2/Ex28_2.PNG diff --git a/2459/CH28/EX28.2/Ex28_2.sce b/2459/CH28/EX28.2/Ex28_2.sce new file mode 100644 index 000000000..fe53d95ce --- /dev/null +++ b/2459/CH28/EX28.2/Ex28_2.sce @@ -0,0 +1,6 @@ +//chapter28
+//example28.2
+//page590
+
+a= dec2bin (23)
+disp(a,'binary equivalent of decimal number 23 = ')
diff --git a/2459/CH28/EX28.3/Ex28_3.PNG b/2459/CH28/EX28.3/Ex28_3.PNG Binary files differnew file mode 100644 index 000000000..bde51fdd3 --- /dev/null +++ b/2459/CH28/EX28.3/Ex28_3.PNG diff --git a/2459/CH28/EX28.3/Ex28_3.sce b/2459/CH28/EX28.3/Ex28_3.sce new file mode 100644 index 000000000..7708f253c --- /dev/null +++ b/2459/CH28/EX28.3/Ex28_3.sce @@ -0,0 +1,6 @@ +//chapter28
+//example28.3
+//page591
+
+a= bin2dec ( ' 110001 ' )
+printf("equivalent decimal of binary 110001 is %d \n",a)
diff --git a/2459/CH28/EX28.4/Ex28_4.PNG b/2459/CH28/EX28.4/Ex28_4.PNG Binary files differnew file mode 100644 index 000000000..ee326d430 --- /dev/null +++ b/2459/CH28/EX28.4/Ex28_4.PNG diff --git a/2459/CH28/EX28.4/Ex28_4.sce b/2459/CH28/EX28.4/Ex28_4.sce new file mode 100644 index 000000000..e6352d36c --- /dev/null +++ b/2459/CH28/EX28.4/Ex28_4.sce @@ -0,0 +1,18 @@ +//chapter28
+//example28.4
+//page598
+
+disp(" A B Y_dash = A + B Y = Y_dash.A ")
+disp(" 0 0 0 0 ")
+disp(" 1 0 1 1 ")
+disp(" 0 1 1 0 ")
+disp(" 1 1 1 1 ")
+
+printf("\nexplanation: \n")
+printf("A=0 and B=0 give A`=1 and B`=1 so Y_dash = A + B is 0 and Y = Y_dash.A is 0 \n")
+
+printf("A=1 and B=0 give A`=0 and B`=1 so Y_dash = A + B is 1 and Y = Y_dash.A is 1 \n")
+
+printf("A=0 and B=1 give A`=1 and B`=0 so Y_dash = A + B is 1 and Y = Y_dash.A is 0 \n")
+
+printf("A=1 and B=1 give A`=0 and B`=0 so Y_dash = A + B is 1 and Y = Y_dash.A is 1 \n")
diff --git a/2459/CH28/EX28.5/Ex28_5.PNG b/2459/CH28/EX28.5/Ex28_5.PNG Binary files differnew file mode 100644 index 000000000..1dfdb46cb --- /dev/null +++ b/2459/CH28/EX28.5/Ex28_5.PNG diff --git a/2459/CH28/EX28.5/Ex28_5.sce b/2459/CH28/EX28.5/Ex28_5.sce new file mode 100644 index 000000000..e36b0a2b0 --- /dev/null +++ b/2459/CH28/EX28.5/Ex28_5.sce @@ -0,0 +1,18 @@ +//chapter28 +//example28.5 +//page598 + +disp(" A B A` Y_dash = A`. B B` Y = Y_dash + B` ") +disp(" 0 0 1 0 1 1 ") +disp(" 1 0 0 0 1 1 ") +disp(" 0 1 1 1 0 1 ") +disp(" 1 1 0 0 0 0 ") + +printf("\nexplanation: \n") +printf("A=0 and B=0 give A`=1 and B`=1 so Y_dash = A`.B is 0 and Y = Y_dash + B` is 1 \n") + +printf("A=1 and B=0 give A`=0 and B`=1 so Y_dash = A`.B is 0 and Y = Y_dash + B` is 1 \n") + +printf("A=0 and B=1 give A`=1 and B`=0 so Y_dash = A`.B is 1 and Y = Y_dash + B` is 1 \n") + +printf("A=1 and B=1 give A`=0 and B`=0 so Y_dash = A`.B is 0 and Y = Y_dash + B` is 0 \n") diff --git a/2459/CH28/EX28.6/Ex28_6.PNG b/2459/CH28/EX28.6/Ex28_6.PNG Binary files differnew file mode 100644 index 000000000..0d6375b24 --- /dev/null +++ b/2459/CH28/EX28.6/Ex28_6.PNG diff --git a/2459/CH28/EX28.6/Ex28_6.sce b/2459/CH28/EX28.6/Ex28_6.sce new file mode 100644 index 000000000..c0a60a6fc --- /dev/null +++ b/2459/CH28/EX28.6/Ex28_6.sce @@ -0,0 +1,15 @@ +// chapter28
+// example28.6
+//page606
+
+printf("Y = A . B . C` . D` + A` . B . C` . D` + A` . B . C . D` + A . B . C . D` \n")
+printf("taking out the common factors \n")
+printf("Y = B . C` . D` . ( A + A` ) + B . C . D` . ( A + A`) \n")
+printf("By theorem 3 \n")
+printf("Y = B . C` . D` + B . C . D` \n")
+printf("again factorize \n")
+printf("Y = B . D` ( C + C` ) \n")
+printf("By theorem 3 \n")
+printf("Y = B . D` . 1 \n")
+printf("thus \n")
+printf("Y = B . D` \n")
diff --git a/2459/CH28/EX28.7/Ex28_7.PNG b/2459/CH28/EX28.7/Ex28_7.PNG Binary files differnew file mode 100644 index 000000000..ea992ddca --- /dev/null +++ b/2459/CH28/EX28.7/Ex28_7.PNG diff --git a/2459/CH28/EX28.7/Ex28_7.sce b/2459/CH28/EX28.7/Ex28_7.sce new file mode 100644 index 000000000..699426835 --- /dev/null +++ b/2459/CH28/EX28.7/Ex28_7.sce @@ -0,0 +1,23 @@ +// chapter28
+// example28.7
+//page606
+
+printf("Y = A . B + A . ( B + C ) + B . ( B + C ) \n")
+printf("By thoerem 14 \n")
+printf("Y = A . B + A . B + A . C + B . B + B .C \n")
+printf("By theorem 6 \n")
+printf("Y= A . B + A . B + A . C + B + B .C \n")
+printf("By theorem 5 \n")
+printf("Y = A . B + A . C + B + B . C \n")
+printf("Factor B out of last 2 terms \n")
+printf("Y = A . B + A . C + B . ( 1 + C ) \n")
+printf("Apply cummulative law and theorem 7 \n")
+printf("Y = A . B + A . C + B . 1 \n")
+printf("Apply theorem 2 \n")
+printf("Y = A . B + A . C + B \n")
+printf("Factor B out of first and third terms \n")
+printf("Y = B . ( A + 1 ) + A . C \n")
+printf("Apply theorem 7 \n")
+printf("Y = B . 1 + A . C \n")
+printf("Apply theorem 2 \n")
+printf("Y = B + A . C \n")
diff --git a/2459/CH28/EX28.8/Ex28_8.PNG b/2459/CH28/EX28.8/Ex28_8.PNG Binary files differnew file mode 100644 index 000000000..7878a8107 --- /dev/null +++ b/2459/CH28/EX28.8/Ex28_8.PNG diff --git a/2459/CH28/EX28.8/Ex28_8.sce b/2459/CH28/EX28.8/Ex28_8.sce new file mode 100644 index 000000000..af6063265 --- /dev/null +++ b/2459/CH28/EX28.8/Ex28_8.sce @@ -0,0 +1,16 @@ +//chapter28 +//example28.8 +//page607 + +printf("i) Y = A + A` . B \n") +printf(" By theorem 16 \n") +printf(" Y = A + A . B + A` . B \n") +printf(" = A + B ( A + A`) \n") +printf(" By theorem 3 \n") +printf(" Y = A + B \n \n") + +printf("ii) Y = A . B + A` . C + B . C \n") +printf(" = A . B + A` . C + B . C ( A + A` )\n") +printf(" = A . B + A` . C + A . B . C + A` . B . C \n") +printf(" = A . B ( 1 + C ) + A` . C( 1 + B ) \n") +printf(" = A . B + A` . C \n") diff --git a/2459/CH28/EX28.9/Ex28_9.PNG b/2459/CH28/EX28.9/Ex28_9.PNG Binary files differnew file mode 100644 index 000000000..b3386ae5f --- /dev/null +++ b/2459/CH28/EX28.9/Ex28_9.PNG diff --git a/2459/CH28/EX28.9/Ex28_9.sce b/2459/CH28/EX28.9/Ex28_9.sce new file mode 100644 index 000000000..626a38a37 --- /dev/null +++ b/2459/CH28/EX28.9/Ex28_9.sce @@ -0,0 +1,8 @@ +//chapter28
+//example28.9
+//page607
+
+printf("Y = ( ( A + B )` . C . D` )` \n")
+printf("Using De Morgan theorem \n")
+printf("Y = ( A + B ) + C` + D \n")
+printf("Y = A + B + C` + D \n")
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