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Number System

Number System. C.I.T. Ch2.5. 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.

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Number System

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  1. Number System C.I.T. Ch2.5

  2. 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

  3. Number System Conversion • Binary to Denary • 10102 • →1 x 23+0 x 22+1 x 21+0 x 20=1110 • Hexadecimal to Denary • 2CA916 • → 2 x 163+12 x 162+10 x 161+9 x 160=1143310

  4. Number System Conversion • Denary to Binary • 3810 2|38….. 2|19…0 2|9…..1 2|4…..1 2|2…..0 1..…0 ∴3810 = 1001102 • Denary to Hexadecimal • 3810 16|38….... 2…6 ∴3810 = 2616

  5. Number System Conversion • Binary to Hexadecimal • 1001 10102 • 10012 = 916 10102 = A16 ∴ 100110102=9A16 • 1010112 • 00102 = 216 10112 = B16 ∴ 1010112=2B16

  6. Number System Conversion • Hexadecimal to Binary • 30D16 • 316 = 00112 016 = 00002 D16 = 11012 ∴ 30D16 = 0011000011012 = 11000011012

  7. Addition of Different Number Systems • Binary • 10102+11102 • 1 0 10 + 1111110 1 1 0 00 ∴ 10102+11102 = 110002 • Hexadecimal • DE16+AB16 • D E + A1 B 1 8 9 ∴ DE16+AB16 = 18916 • E16 + B16 =1916 • D16 + A16+ 116 =1816

  8. Subtraction of Different Number Systems • 102 – 12 = 12 • 02 – 02 = 02 • 102 – 12 = 12 • 102 – 12 = 12 • Binary • 110102-11012 • 1 1110 110 - 1 10 1 1 1 0 1 ∴ 110102-11012 = 110002

  9. Subtraction of Different Number Systems • 1716 – 916 = E16 • A16 – 616 – 116 = 316 • Hexadecimal • A716 - 6916 • A1 7 - 61 9 3 E ∴ A716 - 6916 = 3E16

  10. The End

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