University:
Kentucky State University
Course:
COS 232| Programming I
Academic year:

2021
Views:

192

Pages:

18
Author:

omiliar74be

Numbering Systems Binary System: Number of Symbols: 2 [0, 1] Base: 2 Decimal System: Number of Symbols: 10 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] Base: 10 Octal System: Number of Symbols: 8 [0, 1, 2, 3, 4, 5, 6, 7] Base: 8 Hexadecimal System: Number of Symbols: 16 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F] Base: 16 2^ position ... 2^4 2^3 2^2 2^1 2^0 ... 16 8 4 2 1 Example: 1010 position: 3 2 1 0 1x2³ + 0x2² + 1x2¹ + 0x2⁰ = 8 + 0 + 2 + 0 = 10 **Converting from binary to decimal:** 1. (101101)₂ → ( )₁₀ position: 5 4 3 2 1 0 1 0 1 1 0 1 64+0+8+4+0+1 = 93 2. (101.11)₂ → ( )₁₀ position: 2 1 0 . -1 -2 1 0 1 . 1 1 4 + 0 + 1 + 0.5 + 0.25 = 5.75 3. (1111.111)₂ → ( )₁₀ 1 1 1 1 . 1 1 1 8 + 4 + 2 + 1 + 0.5 + 0.25 + 0.125 = 15.875 **Converting from decimal to binary:** 1. (12)₁₀ → ( )₂ 12: 8 4 2 1 1 1 0 0 (1100)₂ **2's complement:** 2's complement = 1's complement + 1 **1's complement:** [Image of a diagram showing the process of inverting bits] **Examples using 2's complement:** **12-6:** 12: 00001100 -6: 11111010 + ----------- 100000110 Ignore the carry bit 00000110 **12+6:** 12: 00001100 +6: 00000110 ----------- 00001010