What is the Number System ?
Number System
What is the Number System ?
Machine doesn't grasp human language because it's subjective. Yet numbers are not random, which is why we use numbers to interact with computers and devices. Number Framework is a system in which we can interact and comprehend the computer. For eg, 0 is OFF for a machine and 1 is ON
Number System definition
In computers, the Number System is defined as a writing system that represents numbers in various ways , i.e. we use different symbols and notations to represent numbers. There are four ways in which we can interpret the number. That is, there are four types of number system: binary, integer, octal, hexadecimal. Let's see each number scheme one by one.
Types of Number System
- Decimal number system (Base- 10)
- Binary number system (Base- 2)
- Octal number system (Base-8)
- Hexadecimal number system (Base- 16)
- Decimal numbers are made of decimal digits: (0,1,2,3,4,5,6,7,8,9)
- But how many items does a decimal number represent?
- 8653 = 8x103 + 6x102 + 5x101 + 3x100
- What about fractions?
- 97654.35 = 9x104 + 7x103 + 6x102 + 5x101 + 4x100 + 3x10-1 + 5x10-2
- In formal notation -> (97654.35)10
- Binary numbers are made of binary digits (bits)
- 0 and 1
How many items does a binary number represent?
- (1011)2 = 1x23 + 0x22 + 1x21 + 1x20 = (11)10
What about fractions?
- (110.10)2 = 1x22 + 1x21 + 0x20 + 1x2-1 + 0x2-2
- Groups of eight bits are called a byte
- (11001001) 2
- Groups of four bits are called a nibble.
- (1101)
Uses of Binary Number
- Easy to represent 0 and 1 using electrical values.
- Possible to tolerate noise.
- Easy to transmit data
- Easy to build binary circuits.
- Divide decimal number by the base (e.g. 2)
- The remainder is the lowest-order digit
- Repeat the first two steps until no divisor remains.
Convert a Fraction from Decimal to Another Base
For each digit position:
- Multiply decimal number by the base (e.g. 2)
- The integer is the highest-order digit
- Repeat the first two steps until the fraction becomes zero.
Integer Fraction Coefficient
0.625 x 2 = 1 + 0.25 a-1 = 1
0.250 x 2 = 0 + 0.50 a-2 = 0
0.500 x 2 = 1 + 0 a-3 = 1
Answer (0.625)10 = (0.a-1 a-2 a-3 )2 = (0.101)2
Number system that has 16 numerals
In mathematics and computing, hexadecimal (also base 16, or hex) is a positional system that represents numbers using a base of 16.
What is a computer Number system?
Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system. Computer architecture supports following number systems.