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01100100111110000011100110100101111100011000011100001110000001111110000000= 0110100111000011100001000011001
0110010011111000001110011010= 010111110011001100011000011100001110000001111110000000011010011100001110000= 1000011001
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01100100111110000011100110100101111100011000011100001110000001111110000000= 0110100111000011100001000011001
01100100111110000011100110100101111100011000011100001110000001111110000000= 0110100111000011100001000011001
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0110010011111000001= 110011010010111110001100001110000111000000111111000000001101001110000111000= 01000011001
0110010011111000001= 110011010010111110001100001110000111000000111111000000001101001110000111000= 01000011001
Binary Numbers
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01100100111110000011100110100101111100011= 0000111000011100000011111100000000110100111000011100001000011001
01100100111110000011100110100101111100011= 0000111000011100000011111100000000110100111000011100001000011001
Binary and Denary Recap
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0110010011111000001= 110011010010111110001100001110000111000000111111000000001101001110000111000= 01000011001
011001001111100000111001101= 001011111001100110001100001110000111000000111111000000001101001110000111000= 01000011001
Denary
•Denary is the number system we use, base 10.
•We have 10 possible digits, 0-9.
•Each digit in a number has a different place value, working from the right hand side place value increases in powers of 10. =
•For example… with the denary number 5106
•
•
•
•
•And so is made up of
<= span style=3D'font-size:120%;font-weight:normal'>•(5Χ1000)+(1Χ<= span lang=3DEN-US style=3D'mso-bidi-font-family:"Courier New";font-size:120%; color:#66CCFF;mso-color-index:6'>100)+(0Χ10)+(6Χ<= span lang=3DEN-US style=3D'mso-bidi-font-family:"Courier New";font-size:120%; color:#66CCFF;mso-color-index:6'>1) =3D 5106
100
101
102
103
5
1000
6
0
1
1
10
100
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01100100111110000011100110100101111100011= 0000111000011100000011111100000000110100111000011100001000011001
0110010011111000001110011010010111110011001100011000011100001110000001111= 1100000000110100111000011100001000011001
Binary
•Binary is the sy= stem used by electronics, i.e. a circuit is either on or off.
•Binary has just two possible digits, 1 or 0. <= /span>
•Each digit in a = number has a different place value, working from the right hand side place value increases in powers of 2.
•For example, the binary 1011 is…
•
•
•
•
•And so is made up of
•(1Χ8)+(0Χ4)+(1Χ2)+(1Χ1)=3D 11
20
21
22
23
1
8
1
1
0
1
2
4
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01100100111110000011100110100101111100011= 0000111000011100000011111100000000110100111000011100001000011001
0110010011111000001110011010010111110011001100011000011100001110000001111= 1100000000110100111000011100001000011001
Binary to Denary
•So to convert fr= om binary to denary you add up the value of each digit.
•
•
•
•
•
•
•The value in denary is…
•= (1Χ128)  = =3D 128
•= (<= /span>1Χ64)   =3D 64
•= (<= /span>0Χ32)   =3D 0
•= (<= /span>0Χ16)   =3D 0
•= (<= /span>1Χ8)    =3D 8
•= (<= /span>0Χ4)    =3D 0
•= (<= /span>0Χ2)    =3D 0
•= (<= /span>1Χ1)    =3D 1
•
•<= /span>To= tal is 128 + 64 += 0 + 0 + 8 + 0 + 0 + 1 =3D 201
1
1
20
Den.
0
16
24
0
32
25
1
64
26
1
128
27
21
22
23