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POWER School
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Unitary System
Unitary System
Decimal System
Unitary System
Decimal System
Binary System
Board Work
Board Work
1.) 155
2.) 165
3.) 185
10
10
10
2
2
2
Board Work
1.) 1100101
2.) 10111101
3.) 1111011
2
2
2
10
10
10
Decimal to Binary Conversion
Decimal to Binary Conversion
of Fraction
Decimal to Binary Conversion
of Fraction
Example:
Decimal to Binary Conversion
of Fraction
Convert 0.375 (base 10) to its
binary equivalent
Example:
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.375
x 2
0.375
x 2
0.375
x 2
0
0.375
x 2
1
0
0.375
x 2
1
0
0.375
x 2
1
0
0.375
x 2
1
05
0.375
x 2
11
05
0.375
x 2
11
05
0.375
x 2
11
05
0.375
x 2
11
057
0.375
x 2
11
057
0.375
x 2
11
0570
0.375
x 2
0570.
0.375
x 2
0570.
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5 1
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5 1
0.5 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5 1
0.5 x 2 1.0
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5 1
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.375 x 2 0.75 0
0.75 x 2 1.5 1
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Fraction
0.375 (base 10) is equal to
0.011 (base2)
Decimal to Binary Conversion
of Fraction
Convert 0.625 (base 10) to its
binary equivalent
Example:
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Fraction
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Fraction
0.625 (base 10) is equal to
0.101 (base2)
Decimal to Binary Conversion
of Fraction
21010.
Decimal to Binary Conversion
of Fraction
1012
Decimal to Binary Conversion
of Fraction
Convert 0.8 (base 10) to its
binary equivalent
Example:
Decimal to Binary Conversion
Decimal to Binary Conversion
of Real Values
Decimal to Binary Conversion
of Real Values
Example:
Convert 6.625 (base 10) to its
binary equivalent
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1.5
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1 1
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1 1
1/2
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1 1
1/2 0.5
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1 1
1/2 0 1
Decimal to Binary Conversion
of Real Values
Division Quotients Remainders
6/2 3 0
3/2 1 1
1/2 0 1
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Real Values
Multiplication Product Integral Parts
0.625 x 2 1.25 1
0.25 x 2 0.5 0
0.5 x 2 1.0 1
Decimal to Binary Conversion
of Real Values
6 (base10)=110 (base2)
Decimal to Binary Conversion
of Real Values
0.625(base10)=0.101(Base2)
Decimal to Binary Conversion
of Real Values
110 (base2)
Decimal to Binary Conversion
of Real Values
0.101 (base2)
Decimal to Binary Conversion
of Real Values
110.101 (base2)
Decimal to Binary Conversion
of Real Values
Binary to Decimal Conversion
of Real Values
Binary to Decimal Conversion
of Real Values
Example:
Convert 0.101 (base 2) to its
decimal equivalent
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
0.5
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
0.5 0
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
0.5 0 0.125
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
0.5 0 0.125+ +
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
1 0 1x2 x2 x2+ +
1 2 3- - -
1/2 + 0 + 1/8
0.5 0 0.125+ +
18
18 .
18 .0
18 .
.
0
18 .
.
0
1
18 .
.
0
1
8
18 .
.
0
1
8
2
18 .
.
0
1
8
20
18 .
.
0
1
8
20
2
18 .
.
0
1
8
20
2
16
18 .
.
0
1
8
20
2
16
18 .
.
0
1
8
20
2
16
10
18 .
.
0
1
8
20
2
16
10
4
18 .
.
0
1
8
20
2
16
10
4
1
18 .
.
0
1
8
20
2
16
10
4
1
0
18 .
.
0
1
8
20
2
16
10
4
1
0 0
18 .
.
0
1
8
20
2
16
10
4
1
0 0
5
18 .
.
0
1
8
20
2
16
10
4
1
0 0
5
40
18 .
.
0
1
8
20
2
16
10
4
1
0 0
5
40
18 .
.
0
1
8
20
2
16
10
4
1
0 0
5
40
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
0.5
0
0.125+
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
0.5
0
0.125+
0.625
Binary to Decimal Conversion
of Real Values
Example: 0.101 (base 2)
0.5
0
0.125+
0.625
Binary Addition
Binary Addition
0 + 0 = 0
Binary Addition
0 + 0 = 0
0 + 1 = 1
Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 =
Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0
Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0Plus a carry over of 1
Example:
101
101+
Example:
101
101+
5
5+
=
Example:
101
101+
5
5+
10
Example:
101
101+
Example:
101
101+
Example:
101
101+
0
Example:
101
101+
0
1
Example:
101
101+
0
1
Example:
101
101+
0
1
Example:
101
101+
0
1
Example:
101
101+
0
1
1
Example:
101
101+
0
1
1
Example:
101
101+
0
1
1
Example:
101
101+
0
1
10
Example:
101
101+
0
1
10
1
Example:
101
101+
0
1
10
1
1
Example:
101
101+
0
1
10
1
1
Example:
+
1011
1001
1001
Example:
+
1011
1001
1001
Example:
+
1011
1001
1001
Example:
+
1011
1001
1001
0
Example:
+
1011
1001
1001
0
1
Example:
+
1011
1001
1001
0
1
Example:
+
1011
1001
1001
0
1
1
Example:
+
1011
1001
1001
0
1
1
Example:
+
1011
1001
1001
0
1
1
Example:
+
1011
1001
1001
0
1
1
0
Example:
+
1011
1001
1001
0
1
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
Example:
+
1011
1001
1001
0
1
1
0
1
0
Example:
+
1011
1001
1001
0
1
1
0
1
0
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
0
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
0
1
Example:
+
1011
1001
1001
0
1
1
0
1
0
1
1
0
1
Example:
+
1011
1001
1001
0
1
0
1
1
0
1
1011
Example:
+
1011
1001
1001
0
1
0
1
1
0
1
10111
Example:
+
1011
1001
1001
0
1
0
1
1
0
1
10111
Quiz
1.) 1011.1011
2.) 1110.011
3.) 67.0625
4.) 0.6875
5.)100111+10101
6.)10111+101101
+111011+10001
7.)10111+111011
+11101011+1101

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Introduction to Computer Lesson 6.0

Editor's Notes

  1. We discuss the different (CLICK NEXT TO CONTIUE)
  2. Like (CLICK NEXT TO CONTIUE)
  3. Or Tally system (CLICK NEXT TO CONTIUE)
  4. The Base 10 Number System And (CLICK NEXT TO CONTIUE)
  5. The Base 2 Number System. We also discuss the conversion of decimal to binary and vice versa. Now guys I have a (CLICK NEXT TO CONTIUE)
  6. I need 3 students. (CLICK NEXT TO CONTIUE)
  7. Answer 1.) 10011011 2.) 10100101 3.) 10111001 I need another 3 students To answer the new board work. (CLICK NEXT TO CONTIUE)
  8. Answer 1.) 101 2.) 189 3.) 123 Now guys lets proceed to another topic. (CLICK NEXT TO CONTIUE)
  9. (CLICK NEXT TO CONTIUE)
  10. We can also convert a decimal fractions to its binary equivalent. The conversion may be accomplished using several techniques. a simpler method consists of repeatedly doubling the decimal fraction and noting the integral part of the product. The conversion ends when zero fractional part is encountered. The binary equivalent consist of the integral part listed from left to right (or top to bottom) (CLICK NEXT TO CONTIUE)
  11. (CLICK NEXT TO CONTIUE)
  12. (CLICK NEXT TO CONTIUE)
  13. (CLICK NEXT TO CONTIUE)
  14. (CLICK NEXT TO CONTIUE)
  15. (CLICK NEXT TO CONTIUE)
  16. (CLICK NEXT TO CONTIUE)
  17. (CLICK NEXT TO CONTIUE)
  18. (CLICK NEXT TO CONTIUE)
  19. (CLICK NEXT TO CONTIUE)
  20. (CLICK NEXT TO CONTIUE)
  21. (CLICK NEXT TO CONTIUE)
  22. (CLICK NEXT TO CONTIUE)
  23. (CLICK NEXT TO CONTIUE)
  24. (CLICK NEXT TO CONTIUE)
  25. (CLICK NEXT TO CONTIUE)
  26. (CLICK NEXT TO CONTIUE)
  27. (CLICK NEXT TO CONTIUE)
  28. (CLICK NEXT TO CONTIUE)
  29. (CLICK NEXT TO CONTIUE)
  30. (CLICK NEXT TO CONTIUE)
  31. (CLICK NEXT TO CONTIUE)
  32. (CLICK NEXT TO CONTIUE)
  33. (CLICK NEXT TO CONTIUE)
  34. (CLICK NEXT TO CONTIUE)
  35. (CLICK NEXT TO CONTIUE)
  36. (CLICK NEXT TO CONTIUE)
  37. Therefore (CLICK NEXT TO CONTIUE)
  38. (CLICK NEXT TO CONTIUE)
  39. (CLICK NEXT TO CONTIUE)
  40. (CLICK NEXT TO CONTIUE)
  41. (CLICK NEXT TO CONTIUE)
  42. (CLICK NEXT TO CONTIUE)
  43. (CLICK NEXT TO CONTIUE)
  44. (CLICK NEXT TO CONTIUE)
  45. (CLICK NEXT TO CONTIUE)
  46. (CLICK NEXT TO CONTIUE)
  47. (CLICK NEXT TO CONTIUE)
  48. (CLICK NEXT TO CONTIUE)
  49. Therefore guy (CLICK NEXT TO CONTIUE)
  50. (CLICK NEXT TO CONTIUE)
  51. (CLICK NEXT TO CONTIUE)
  52. Questions guys?? Sometimes we have a non terminating fractions. Meaning endless yung computation. (CLICK NEXT TO CONTIUE)
  53. (CLICK NEXT TO CONTIUE)
  54. We also have a (CLICK NEXT TO CONTIUE)
  55. Converting a real number in base 10 to its binary equivalent is just a matter of Combining decimal to binary conversation Of whole numbers and fractional number. Here is a sample. (CLICK NEXT TO CONTIUE)
  56. Here are the steps. 1st convert the decimal whole number. (CLICK NEXT TO CONTIUE)
  57. (CLICK NEXT TO CONTIUE)
  58. (CLICK NEXT TO CONTIUE)
  59. (CLICK NEXT TO CONTIUE)
  60. (CLICK NEXT TO CONTIUE)
  61. (CLICK NEXT TO CONTIUE)
  62. (CLICK NEXT TO CONTIUE)
  63. (CLICK NEXT TO CONTIUE)
  64. (CLICK NEXT TO CONTIUE)
  65. (CLICK NEXT TO CONTIUE)
  66. 2nd step is to convert the fractional part (CLICK NEXT TO CONTIUE)
  67. (CLICK NEXT TO CONTIUE)
  68. (CLICK NEXT TO CONTIUE)
  69. (CLICK NEXT TO CONTIUE)
  70. (CLICK NEXT TO CONTIUE)
  71. (CLICK NEXT TO CONTIUE)
  72. (CLICK NEXT TO CONTIUE)
  73. (CLICK NEXT TO CONTIUE)
  74. (CLICK NEXT TO CONTIUE)
  75. (CLICK NEXT TO CONTIUE)
  76. (CLICK NEXT TO CONTIUE)
  77. (CLICK NEXT TO CONTIUE)
  78. (CLICK NEXT TO CONTIUE)
  79. (CLICK NEXT TO CONTIUE)
  80. (CLICK NEXT TO CONTIUE)
  81. We can check the decimal to binary Conversion of real values by using The counter conversion. And that is (CLICK NEXT TO CONTIUE)
  82. We can check the decimal to binary Conversion of real values by using The counter conversion. That is called. (CLICK NEXT TO CONTIUE)
  83. The expanded notation method is still used in binary to decimal conversion of real values. This time however, the place values of the fractional part are equal the variety of the fractional are equal to the negative powers of two. (CLICK NEXT TO CONTIUE)
  84. (CLICK NEXT TO CONTIUE)
  85. (CLICK NEXT TO CONTIUE)
  86. (CLICK NEXT TO CONTIUE)
  87. (CLICK NEXT TO CONTIUE)
  88. (CLICK NEXT TO CONTIUE)
  89. (CLICK NEXT TO CONTIUE)
  90. (CLICK NEXT TO CONTIUE)
  91. (CLICK NEXT TO CONTIUE)
  92. (CLICK NEXT TO CONTIUE)
  93. (CLICK NEXT TO CONTIUE)
  94. Pano nakuha yung answer na 0.125? By dividing 1 over 8. (CLICK NEXT TO CONTIUE)
  95. One divided by 8 ay cannot be. So what shall we do? We will put a point (.) (CLICK NEXT TO CONTIUE)
  96. And then we will add a (CLICK NEXT TO CONTIUE)
  97. Zero. Ten divided by eight (CLICK NEXT TO CONTIUE)
  98. Ooppps lagay muna tayo ng point sa taas. Baka maligaw tayo eh. (CLICK NEXT TO CONTIUE)
  99. One times eight? (CLICK NEXT TO CONTIUE)
  100. Ten minus eight? (CLICK NEXT TO CONTIUE)
  101. Two divided by eight? Cannot be. So we will add another zero. (CLICK NEXT TO CONTIUE)
  102. Twenty divided by eight? (CLICK NEXT TO CONTIUE)
  103. Two times eight? (CLICK NEXT TO CONTIUE)
  104. And then, what is next?? (CLICK NEXT TO CONTIUE)
  105. We will subtract. Zero minus six? Cannot be. We will borrow one from two. (CLICK NEXT TO CONTIUE)
  106. Ten minus six? (CLICK NEXT TO CONTIUE)
  107. Answer is four Then the two will become one. (CLICK NEXT TO CONTIUE)
  108. One minus one? We will get the answer of (CLICK NEXT TO CONTIUE)
  109. We can also subtract sixteen to twenty. And still the answer is four. Now four divided by eight? Cannot be. So we will add another zero. (CLICK NEXT TO CONTIUE)
  110. Forty divided by eight? (CLICK NEXT TO CONTIUE)
  111. The answer is five. Then Five times eight? (CLICK NEXT TO CONTIUE)
  112. The answer is forty. Then we will subtract. (CLICK NEXT TO CONTIUE)
  113. Forty minus forty? The answer is zero. Na hindi na kasya.. What is the final answer? (CLICK NEXT TO CONTIUE)
  114. So let’s continue the computation. (CLICK NEXT TO CONTIUE)
  115. (CLICK NEXT TO CONTIUE)
  116. (CLICK NEXT TO CONTIUE)
  117. That is the final answer. Question guys?? Now let’s proceed to (CLICK NEXT TO CONTIUE)
  118. Binary addition is simple to learn it only involves two characters – 0 and 1. It is no different from decimal number addition. Adding these two numbers will result only 4 possible combinations and they are as follows: (CLICK NEXT TO CONTIUE)
  119. (CLICK NEXT TO CONTIUE)
  120. (CLICK NEXT TO CONTIUE)
  121. (CLICK NEXT TO CONTIUE)
  122. (CLICK NEXT TO CONTIUE)
  123. (CLICK NEXT TO CONTIUE)
  124. (CLICK NEXT TO CONTIUE)
  125. (CLICK NEXT TO CONTIUE)
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  127. (CLICK NEXT TO CONTIUE)
  128. (CLICK NEXT TO CONTIUE)
  129. (CLICK NEXT TO CONTIUE)
  130. (CLICK NEXT TO CONTIUE)
  131. (CLICK NEXT TO CONTIUE)
  132. (CLICK NEXT TO CONTIUE)
  133. (CLICK NEXT TO CONTIUE)
  134. (CLICK NEXT TO CONTIUE)
  135. (CLICK NEXT TO CONTIUE)
  136. (CLICK NEXT TO CONTIUE)
  137. (CLICK NEXT TO CONTIUE)
  138. (CLICK NEXT TO CONTIUE)
  139. (CLICK NEXT TO CONTIUE)
  140. (CLICK NEXT TO CONTIUE)
  141. Question guys??? (CLICK NEXT TO CONTIUE)
  142. Question guys??? (CLICK NEXT TO CONTIUE)
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  169. Clear?? Question?? Clarification?? (CLICK NEXT TO CONTIUE)
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