Number System & Boolean Algebra SN-2 Notes

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What are the wide variety structures?
Range systems are the approach to represent numbers in the laptop system structure, each fee that you are saving or moving into/from laptop memory has a defined number system.

Laptop architecture supports following variety systems.

Binary range device
Octal variety device
Decimal wide variety system
Hexadecimal (hex) quantity system
1) Binary quantity device
A Binary number machine has handiest two digits which might be zero and 1. Each variety (fee) represents with 0 and 1 in this wide variety gadget. The base of binary quantity gadget is 2, as it has simplest two digits.

2) Octal range device
Octal range device has simplest 8 (eight) digits from 0 to 7. Each range (cost) represents with 0,1,2,3,4,5,6 and seven in this quantity device. The base of octal range gadget is eight, as it has handiest eight digits.

3) Decimal range system
Decimal quantity gadget has best ten (10) digits from zero to 9. each quantity (fee) represents with 0,1,2,three,four,5,6, 7,8 and nine on this variety system. The bottom of decimal range machine is 10, because it has handiest 10 digits.

Four) Hexadecimal variety system
A Hexadecimal wide variety device has 16 (sixteen) alphanumeric values from 0 to nine and A to F. each wide variety (value) represents with zero,1,2,three,four,five,6, 7,8,nine,A,B,C,D,E and F on this wide variety system. The bottom of hexadecimal variety device is 16, as it has sixteen alphanumeric values. Here A is 10, B is eleven, C is 12, D is thirteen, E is 14 and F is 15.
Quantity gadget Conversions
There are 3 kinds of conversion:
Decimal number machine to different Base
[For example: Decimal Number System to Binary Number System]
Other Base to Decimal number machine
[For example: Binary Number System to Decimal Number System]
Other Base to different Base
[For example: Binary Number System to Hexadecimal Number System]
Decimal wide variety device to other Base
To convert wide variety gadget from Decimal range machine to another Base is quite clean; you need to observe just steps:
A) Divide the range (Decimal variety) with the aid of the bottom of goal base system (in which you want to transform the number: Binary (2), octal (eight) and Hexadecimal (sixteen)).
B) Write the rest from step 1 as a Least Signification Bit (LSB) to Step remaining as a most sizable Bit (MSB). Other Base gadget to Decimal quantity Base
To transform wide variety gadget from another Base system to Decimal variety machine, you need to follow simply 3 steps:
A) Determine the base price of source quantity device (which you want to transform), and additionally decide the placement of digits from LSB (first digit’s role – 0, second digit’s position – 1 and so on).
B) Multiply each digit with its corresponding multiplication of role fee and Base of source quantity system’s Base.
C) Upload the resulted price in step-B.
Explanation regarding examples:
Underneath given assessments contains the subsequent rows:
A) Row 1 carries the DIGITs of number (this is going to be transformed).
B) Row 2 contains the placement of every digit within the quantity machine.
C) Row three contains the multiplication: DIGIT* BASE^function.
D) Row four includes the calculated end result of step C.
E) After which add each value of step D, resulted cost is the Decimal range.