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Number System C.I.T. Ch2.5

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Denary, Binary, Hexadecimal Number System Denary Number System Ten is it’s base. Ten distinct values :0,1,2,3,4,5,6,7,8,9 Binary Number System Two is it’s base. Two distinct values :0,1 Hexadecimal Number System Sixteen is it’s base. Sixteen distinct values : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

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Number System Conversion Binary to Denary 1010 2 →1 x 2 3 +0 x 2 2 +1 x 2 1 +0 x 2 0 =11 10 Hexadecimal to Denary 2CA9 16 → 2 x 16 3 +12 x 16 2 +10 x 16 1 +9 x 16 0 =11433 10

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Number System Conversion Denary to Binary 38 10 2|38….. 2|19…0 2|9…..1 2|4…..1 2|2…..0 1..…0 ∴ 38 10 = 100110 2 Denary to Hexadecimal 38 10 16|38….... 2…6 ∴ 38 10 = 26 16

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Number System Conversion Binary to Hexadecimal 1001 1010 2 1001 2 = 9 16 1010 2 = A 16 ∴ 10011010 2 =9A 16 101011 2 0010 2 = 2 16 1011 2 = B 16 ∴ 101011 2 =2B 16

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Number System Conversion Hexadecimal to Binary 30D 16 3 16 = 0011 2 0 16 = 0000 2 D 16 = 1101 2 ∴ 30D 16 = 001100001101 2 = 1100001101 2

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Addition of Different Number Systems Binary 1010 2 +1110 2 1 0 10 + 1 1 1 1 1 10 1 1 0 00 ∴ 1010 2 +1110 2 = 11000 2 Hexadecimal DE 16 +AB 16 D E + A 1 B 1 8 9 ∴ DE 16 +AB 16 = 189 16 E 16 + B 16 =19 16 D 16 + A 16 + 1 16 =18 16

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Subtraction of Different Number Systems 10 2 – 1 2 = 1 2 0 2 – 0 2 = 0 2 10 2 – 1 2 = 1 2 Binary 11010 2 -1101 2 1 1 1 1 0 1 1 0 - 1 1 0 1 1 1 0 1 ∴ 11010 2 -1101 2 = 11000 2

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Subtraction of Different Number Systems 17 16 – 9 16 = E 16 A 16 – 6 16 – 1 16 = 3 16 Hexadecimal A7 16 - 69 16 A 1 7 - 6 1 9 3 E ∴ A7 16 - 69 16 = 3E 16

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