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Coding Part 2

Lesson 2 0x002 010. Coding Part 2. Weight of the Digit. Weights Decimal Example (3672) 10 Binary Example (1011) 2. Number of Possibilities. Binary (base= 2). 2. 4. 8. 16. Number of possibilities = (B) n. B : Base n : # of Digits. Number of Possibilities. Decimal (Base =10).

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Coding Part 2

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  1. Lesson 2 0x002010 Coding Part 2

  2. Weight of the Digit • Weights • Decimal Example (3672)10 • Binary Example (1011)2

  3. Number of Possibilities • Binary (base= 2) 2 4 8 16 Number of possibilities = (B)n B : Base n : # of Digits

  4. Number of Possibilities • Decimal (Base =10) 10 1000 100 Number of possibilities = (B)n B : Base n : # of Digits

  5. Number of Possibilities Hexadecimal (Base =16) • Octal(Base =8) Number of possibilities = (B)n Number of possibilities = (B)n 1 Digit Number of possibilities = (8)1 =8 1 Digit Number of possibilities = (16)1 =16 2 Digits Number of possibilities = (8)2 =64 2 Digits Number of possibilities = (16)2 =256 5 Digits Number of possibilities = (8)5 = 32768 5 Digits Number of possibilities = (16)5 = 11029518992652895256576

  6. Conversion Table • Binary Base =2 = (2)1 • Octal Base = 8= (2)3 • Hexadecimal Base =16 = (2)4 • Their base have number 2 as a common • That’s why • 1 Octal digit equivalent to 3 Binary • 1 Hex digit equivalent to 4 Binary digits * Look at the table and notice binary columns

  7. Binary Addition • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 =10 * Look at the table and notice binary columns

  8. Binary Addition 1 5 1 3 + ----- 28 • How do we do Decimal Addition ? =5+5 =10-B =0 =5+7 =12 –B =2 1 1 1 5 1 5 + ----- 30 1 5 1 7 + ----- 32 Case 1: the result is less than Base Case 2: the result equals Base Case 3: the result is higher than Base • Do it for Binary 01 01+ ----- 10 01 01 01+ ----- 11 00 01+ ----- 01

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