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Number Systems,

Conversion between Bases,

and

Basic Binary Arithmetic

(Lecture #1)

Digital Electronics1. Number Systems

2. Binary Arithmetic and Binary Codes

3. Boolean Algebra

4. Basic Logic Gates

5. Boolean Expressions

6. Karnaugh Maps

7. Minimization of Boolean Expressions

8. Analysis and Design of Combinational Logic Circuits

9. Single-bit and Multi-bit Adder Circuits

10. Multiplexers and Demultiplexers

11. Decoders and Encoders

12. Tri-state devices

13. Latches and Flip-Flops

14. Registers and Counters

15. Analysis and Design of Sequential Logic Circuits

16. Memory cells and Memory design

(see syllabus)

Numerical Representation

- Science, Technology, Business all deal with
- Quantities
- Measure, monitored, arithmetically manipulated, recorded……

- Quantities Represented in two ways
- Analogue
- Digital

- Quantities

Analog

- Represented by meter movement proportional to the value of the quantity
- Temperature, voltage, current
- Common mercury thermometer
- Automobile speedometer
- Continuous set of values

Digital representation

- Not by continuous variable indicators but by digits (step by step)
- Digital watch
- Digital speedometer
- Digital temperature gauge

52

- What does this number represent?
- What does it mean?

1011001.101

- What does this number represent?
- Consider the base (or radix) of the number.

Number Systems

- R is the radix or base of the number system
- Must be a positive number
- R digits in the number system: [0 .. R-1]

- Important number systems for digital systems:
- Base 2 (binary): [0, 1]
- Base 8 (octal): [0 .. 7]
- Base 16 (hexadecimal): [0 .. 9, A, B, C, D, E, F]

D = [a4a3a2a1a0.a-1a-2a-3]R

D = decimal value

ai = ith position in the number

R = radix or base of the number

Number SystemsD = an x R4 + an-1 x R3 + … + a0 x R0

+ a-1 x R-1 + a-2 x R-2 + … a-m x R-m

D = decimal value

ai = ith position in the number

R = radix or base of the number

Number Systems
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