Lesson 4 The basics of Data Representation.pptx
- 2. 2 Outline Representing numbers Unsigned Signed Floating point Representing characters & symbols ASCII Unicode
- 3. 3 Data Representation in Computers Data are stored in Registers Registers are limited in number & size With a n-bit register Min value 0 Max value 2n -1 n-1 n-2 ... … ... 2 0 1 n-bits
- 4. 4 Data Representation Data Representation • Represents quality or characteristics • Not proportional to a value • Name, NIC no, index no, Address Qualitative Quantitative • Quantifiable • Proportional to value α • No of students, marks for CS2052, GPA
- 6. 6 Number Systems Decimal number system 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Binary number system 0, 1 Octal number system 0, 1, 2, 3, 4, 5, 6, 7 Hexadecimal number system 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- 7. 7 Quantitative Numbers Integers Unsigned 20 Signed +20, -20 Non-integers Floating point numbers - 10.25, 3.33333…, 1/8 = 0.125
- 8. 8 Signed Integers We need a way to represent negative values 3 representations Sign & Magnitude representation (S&M) Complement method Bias notation or Excess notation
- 9. 9 1. Sign & Magnitude Representation n-bit unsigned magnitude & sign bit (S) If S 0 – Integer is positive or zero 1 – Integer is negative or zero Range –(2n -1) to +(2n -1) sign n-1 ... n-2 ... 2 0 1 Magnitude (n-bits)
- 10. 10 Example – Sign & Magnitude If 8-bit register is used what are min & max numbers? What are 0000 0000 and 1000 0000 in decimal? Representation of zero is not unique
- 11. 11
- 12. 12 Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them.