Data Representation

Question 1

Number Systems

Question 1

Types of Number Systems

Answer 1

1. Decimal
2. Binary
3. Octal
4. Hexadecimal

Question 2

Decimal (Base 10) Number System

Answer 2

• Prefix Deci = Decade = 10 years = base 10
• Also known as the base 10 number system.
• 10 different numbers in the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• It uses 10 distinct symbols (0-9) to represent numbers.
• Each digit’s position in a number represents a power of 10.

eg.) Number 24:
The rightmost digit (‘4’) is in the one’s place. Its value is 4 x 1 = 4.
The left digit (‘2’) is in the tens place. It’s value is 2 x 10^1 = 2 x 10 = 20.
So 4 +20 = 24.

eg.) Number 325:
The rightmost digit (‘5’) is in the “ones” place. It’s value is 5 x 10^0 = 5 x 1 = 5
Moving to the left (‘2’) is in the tens place. It’s value is 2 x 10^1 = 2 x 10 = 20.
Continuing to the left, the leftmost digit (‘3’) is in the hundreds place. It’s value is 3 x 10^2 = 3 x 100 = 300.
So the number ‘325’ is 5 + 20 + 300.

eg.) Number 4589:
9 in one place. Value is 9 x 10^0 = 9 x 1 = 9
8 in tens place. Value is 8 x 10^1 = 8 x 10 = 80
5 in hundreds place. Value is 5 x 10^2 = 5 x 100 = 500
4 in thousands place. Value is 4 x 10^3 = 5 x 1000 = 4000
So 9 + 80 + 500 + 4000 = 4589.

Question 3

Binary (Base 2) Number System:

Answer 3

Binary = 2 = Base 2
Consists of only 2 symbols: 0 and 1.
Each digit’s position in a binary number represents a power of 2.
Starting from the rightmost digit, the positions are power 2^0, 2^1, 2^2, …