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Polynomial Representations of Integers

Polynomial Representations of Integers. Lesson 4.7. Base Notation. A number is written in base b notation , (d n , d n-1 ,d n-2 ,…,d 1 ,d 0 ) b Iff each digit d i is a particular integer from 0 through b – 1, and the value of the number is D n b n + d n-1 b n-1 +…+d 1 b 1 + d 0 b 0.

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Polynomial Representations of Integers

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  1. Polynomial Representations of Integers Lesson 4.7

  2. Base Notation • A number is written in base b notation , (dn, dn-1,dn-2,…,d1,d0)b Iff each digit di is a particular integer from 0 through b – 1, and the value of the number is Dnbn + dn-1bn-1+…+d1b1 + d0b0

  3. Hexadecimal (base 16)Binary (base 2)

  4. Example 1 • Write 3D7B16 in base 10 3(163)+ 13(162)+7(16) + 11(1) 12288+ 3328+ 112+ 11 15739

  5. Example 2 • Write 4387 in base 6. 4387 ÷ 6 = 731 r. 1 731÷ 6 = 121 r. 5 121÷ 6 = 20 r. 1 20 ÷ 6 = 3 r. 2 3 ÷ 6 = 0 r. 3 So, 32,151

  6. Example 3 • Perform the base 2 addition below. 1 0 0 1 1 + 1 1 0 0 0 1 1 0 1 0 1 1

  7. How your computer adds…Half Adder – binary ones digits Sum digit and and p q or not carry digit

  8. Sum digit p q and and carry digit or not

  9. Homework Pages 268 – 269 3, 6 , 8 , 11 – 13, 18

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