lecture 1 and 2: number systems/ code and complements

Analog Representation

• A quantity represented by voltage, current, or meter movement that is proportional to the value of that quantity.

• Characteristics: Continuous.

Digital Representation

• Quantities are represented by symbols called digits.

• Characteristics: Not proportional but represented by discrete values.

Digital Systems

• A combination of devices that manipulate physical quantities or information in digital forms.

• Examples: Digital watch, logic gates.

Analog Systems

• Devices manipulate physical quantities represented in analog form.

• Examples: Amplifiers, analog watch.

• Ease of design.

• Higher resolution and output quality.

• More error/fault tolerance.

• Greater flexibility in design and application.

• Digital signals can be transmitted over long distances.

• Less noise, distortion, and interference.

Advantages of Digital Systems

Codes

represent numbers, letters, or words using a special group of symbols, often for convenience in representing long and complicated numbers or words.

Straight Binary Coding

represents a decimal number by its equivalent binary number.

Binary Coded Decimal (BCD)

represents each digit of a decimal number by its binary equivalent, offering a fast and efficient way to convert decimal numbers into binary.

Excess-3

is a non-weighted BCD code where 3 is added to each decimal digit, and the result is converted to 4-bit BCD.

Gray Code

is an unweighted code where only one bit changes between consecutive values. It is often used in mechanical switching systems.

ASCII (American Standard Code for Information Interchange)

is a 7-bit code that represents 128 possible characters.

binary addition, multiplication, subtraction, and division.

What are the basic binary arithmetic operations?

he 2’s complement of a binary number

is found by subtracting the number from 2n2^n2n (where n is the number of bits), and it's used for representing negative binary numbers.

10’s complement of a decimal number

is found by subtracting the number from 10n10^n10n (where n is the number of digits).

Unsigned binary numbers

represent only positive values

signed binary numbers

use a sign bit (0 for positive, 1 for negative) to indicate the sign.

sign bit

is an extra bit in signed binary numbers that indicates whether the number is positive (0) or negative (1).