Number System Octal Number System

1. By: Vhonz Sugatan
POWER School

2. Last week…

4. Decimal to Binary
Conversion of Fraction

5. Decimal to Binary
Conversion of Real
Values

6. Binary to Decimal
Conversion of Real
Values

7. Binary Addition

8. Binary Subtraction

9. Binary Subtraction
0 - 0 =

10. Binary Subtraction
0 - 0 = 0

11. Binary Subtraction
0 - 0 = 0
1 - 0 =

12. Binary Subtraction
0 - 0 = 0
1 - 0 = 1

13. Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 =

14. Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0

15. Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 =

16. Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 0

17. Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 0 With a borrow of 1

18. Example:

19. Example:
1010

20. Example:
1010
100

21. Example:
1010
100

22. Example:
1010
100

23. Example:
1010
100
0

24. Example:
1010
100
0

25. Example:
1010
100
0

26. Example:
1010
100
10

27. Example:
1010
100
10

28. Example:
1010
100
10

29. Example:
1010
100
10

30. Example:
1010
100
10
2

31. Example:
1010
100
110
2

32. Example:
1010
100
110
20

33. Example:
1010

34. Example:
1010
101

35. Example:
1010
101
101

36. Example:
100011
1111

37. Example:
100011
1111
10100

38. Example:
1000.11
11.01

39. Example:
1000.11
11.01
101.10

40. Example:
10000
1111

41. Example:
10000
1111
1

42. The One’s Compliment Method

43. The One’s Compliment Method
11010

44. The One’s Compliment Method
11010 is 00101

45. The One’s Compliment Method
111101

46. The One’s Compliment Method
111101
000010

47. Example:
110011(Base2)

48. Example:
110011(Base2)
11101(Base2)

49. Step 1:

50. Step 1:
Get the one’s compliment of
subtrahend

51. Step 1:
Get the one’s compliment of
subtrahend.
The one’s compliment of
11101is 00010

52. Step 2:

53. Step 2:
Get the binary sum of the minuend
and the one’s compliment of the
subtrahend.

54. Step 2:
Get the binary sum of the minuend
and the one’s compliment of the
subtrahend.
110011 + 00010 = 110101

55. Step 3:

56. Step 3:
Add the and-around carry by
taking the leftmost digit of the
binary sum and adding it with the
first digit.

57. Step 3:
110101

58. Step 3:
110101

59. Step 3:
10101
1
+

60. Step 3:
10101
1
+
10110

61. Step 3:
10101
1
+
10110

62. Binary Multiplication

63. Binary Multiplication
0 x 0 =

64. Binary Multiplication
0 x 0 = 0

65. Binary Multiplication
0 x 0 = 0
1 x 0 =

66. Binary Multiplication
0 x 0 = 0
1 x 0 = 0

67. Binary Multiplication
0 x 0 = 0
1 x 0 = 0
0 x 1 =

68. Binary Multiplication
0 x 0 = 0
1 x 0 = 0
0 x 1 = 0

69. Binary Multiplication
0 x 0 = 0
1 x 0 = 0
0 x 1 = 0
1 x 1 =

70. Binary Multiplication
0 x 0 = 0
1 x 0 = 0
0 x 1 = 0
1 x 1 = 1

71. Example

72. Example
111

73. Example
111
101x

74. Example
111
101x
111

75. Example
111
101x
111
000

76. Example
111
101x
111
000
111

77. Example
111
101x
111
000
111+

78. Example
111
101x
111
000
111+
100011

79. Example
101

80. Example
101
101x

81. Example
101
101x
101

82. Example
101
101x
101
000

83. Example
101
101x
101
000
101

84. Example
101
101x
101
000
101+

85. Example
101
101x
101
000
101+
11001

86. Example 11.00

87. Example 11.00
10.10x

88. Example 11.00
10.10x
00 00

89. Example 11.00
10.10x
00 00
110 0

90. Example 11.00
10.10x
00 00
110 0
0000

91. Example 11.00
10.10x
00 00
110 0
0000
1100

92. Example 11.00
10.10x
00 00
110 0
0000
1100+

93. Example 11.00
10.10x
00 00
110 0
0000
1100+
1111000

94. Example 11.00
10.10x
00 00
110 0
0000
1100+
111.1000

95. Binary Division

96. Binary Division
0 / 1 =

97. Binary Division
0 / 1 = 0

98. Binary Division
0 / 1 = 0
1 / 1 =

99. Binary Division
0 / 1 = 0
1 / 1 = 1

100. Binary Division
0 / 1 = 0
1 / 1 = 1
1 / 0 =

101. Binary Division
0 / 1 = 0
1 / 1 = 1
1 / 0 = is undefined

102. Example
100 1100

103. Example
100 1100

104. Example
100 1100

105. Example
100 1100

106. Example
100 1100
1

107. Example
100 1100
1
100

108. Example
100 1100
1
100-

109. Example
100 1100
1
100-
10

110. Example
100 1100
1
100-
100

111. Example
100 1100
11
100-
100

112. Example
100 1100
11
100-
100
100

113. Example
100 1100
11
100-
100
100-

114. Example
100 1100
11
100-
100
100-
000

115. The Octal Number
System

116. Decimal to Octal Conversion

117. Decimal to Octal Conversion
Example:
Convert 56(base 10) to its octal
equivalent.

118. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8

119. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7

120. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7 0

121. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7 0
7 / 8

122. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7 0
7 / 8 0

123. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7 0
7 / 8 0 7

124. Decimal to Octal Conversion
Example:
Division Quotients Remainders
56 / 8 7 0
7 / 8 0 7

125. Decimal to Octal Conversion
Example:
56(base 10) is equivalent to
70(base8)

126. Decimal to Octal Conversion
568
7
56
0

127. Decimal to Octal Conversion
8 7

128. Decimal to Octal Conversion
8 7.0

129. Decimal to Octal Conversion
8 7.0
0.

130. Decimal to Octal Conversion
8 7.0
0.8

131. Decimal to Octal Conversion
8 7.0
0.8
64

132. Decimal to Octal Conversion
8 7.0
0.8
64

133. Decimal to Octal Conversion
8 7.0
0.8
64
6

134. Decimal to Octal Conversion
8 7.00
0.8
64
60

135. Decimal to Octal Conversion
8 7.00
0.87
64
60

136. Decimal to Octal Conversion
8 7.00
0.87
64
60
56

137. Decimal to Octal Conversion
8 7.00
0.87
64
60
56

138. Decimal to Octal Conversion
8 7.00
0.87
64
60
56
4

139. Decimal to Octal Conversion
8 7.000
0.87
64
60
56
40

140. Decimal to Octal Conversion
8 7.000
0.875
64
60
56
40

141. Decimal to Octal Conversion
8 7.000
0.875
64
60
56
40
40

142. Decimal to Octal Conversion
8 7.000
0.875
64
60
56
40
40
0

143. Decimal to Octal Conversion
Seat Work

144. Decimal to Octal Conversion
Seat Work
1.) 171 base10 to base8
2.) 1254 base10 to base8
3.) 1573 base10 to base8

145. Octal to Decimal Conversion

146. Octal to Decimal Conversion
Example:
Convert 70(base 8) to its decimal
equivalent.

147. Octal to Decimal Conversion
Example:
70 base8
7 0

148. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8

149. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+

150. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+
01

151. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+
01
0

152. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+
01
056

153. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+
01
56 + 0

154. Octal to Decimal Conversion
Example:
70 base8
7 0x8 x8+
01
56 +
56
0

155. Octal to Decimal Conversion
Example:
Convert 36471(base 8) to its
decimal equivalent.

156. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234

157. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
1

158. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
156

159. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
156256

160. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
1562563072

161. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
156256307212288

162. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
156256307212288 ++++

163. Octal to Decimal Conversion
Example:
3x8+6x8+4x8+7x8+1x8
01234
156256307212288 ++++
= 15673

164. Octal to Binary Conversion

165. Octal to Binary Conversion
OCTAL
NUMBER
BINARY
EQUIVALENT
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

166. Octal to Binary Conversion
Example:

167. Octal to Binary Conversion
Example:
Convert 13(base 8) to its binary
equivalent.

168. Octal to Binary Conversion
Example:
1 (base8) in binary is equal to 001

169. Octal to Binary Conversion
Example:
1 (base8) in binary is equal to 001
3 (base8) in binary is equal to 011

170. Octal to Binary Conversion
Example:
1 (base8) in binary is equal to 001
3 (base8) in binary is equal to 011
Therefore 13 (base8) is equal
to 001011 or 1011

171. Octal to Binary Conversion
Example:
Convert 765(base 8) to its binary
equivalent.

172. Octal to Binary Conversion
Example:
7 (base8) to binary is 111

173. Octal to Binary Conversion
Example:
7 (base8) to binary is 111
6 (base8) to binary is 110

174. Octal to Binary Conversion
Example:
7 (base8) to binary is 111
6 (base8) to binary is 110
5 (base8) to binary is 101

175. Octal to Binary Conversion
Example:
7 (base8) to binary is 111
6 (base8) to binary is 110
5 (base8) to binary is 101
Therefore 765 (base8) is equal to
111110101

176. Binary to Octal Conversion

177. Binary to Octal Conversion
Example:
Convert 10101010(base2) to its
octal equivalent.

178. Binary to Octal Conversion
Step 1:
Arrange the binary into groups of 3.

179. Binary to Octal Conversion
Step 1:
Arrange the binary into groups of 3.
10101010

180. Binary to Octal Conversion
Step 1:
Arrange the binary into groups of 3.
10101010

181. Binary to Octal Conversion
Step 2:
For each group, convert each digit
to decimal by multiplying it by its
positional value.

182. Binary to Octal Conversion
Step 2:
GROUP CONVERSION TO OCTAL
010 0x2+1x2+0x2 = 2
101 1x2+0x2+1x2 = 5
10 1x2+0x2 = 2

183. Binary to Octal Conversion
Step 2:
GROUP CONVERSION TO OCTAL
010 0x2+1x2+0x2 = 2
101 1x2+0x2+1x2 = 5
10 1x2+0x2 = 2

184. Binary to Octal Conversion
Therefore the 10101010 (base2)
is equivalent to 252 (base8)

185. The Hexadecimal
Number System