Tutorial 1: Number Systems and Codes

[HatchSuper Moderator]

A number system is formed by selecting a set of symols to represent numericl values. The number of symbols used is clled the base or radix of that number system. The decimal number system contains ten unique symbols: 0. 1, 2, 3, 4, 5, 6, 7, 8, 9. It does not contain a symbol for "ten" rather above as a combintion of other symbols. Since it has ten symbols its base or radix is 10.

Note that each of the symbols indicates a different numerical quantity. Where 0 is the smalles quantity, 9 is the largest quantity. 

Since the decimal number symbol has limited nase symbols (just 10), and we cannot express every quantity nedded in mathematics and science, digit notation is used. Here, the value of a symbol depends on its location in the number. The positional value of a fdigit is known as its weight.

For instance, in the number 635.43, the symbol 3 occurs in two location but because the weights of the digits in which 3 lies are different, each takes on a different positional value. 

Table below shows some digit locations f the deciaml number system and the corresponding weights. Here, the table digit notation and weight.

103	102	101	100	.	10-1	10-2	10-3
1000	100	10	1	.	1/10	1/100	1/1000

digit just to the left of the decimal point is used as the reference digit and its weight is 10⁰ or 1. The decimal weights are formed by raising the base of the number system to a power. The exponent or power of the weight can be positive or negative. The value of this exponent is found by connecting the number of digits to the of the reference digit. All digits to the left of the reference digit are considered to have a weight with +ve exponent of the power of 10. While weight of digits to the weight of the reference digits have -ve exponent as illusted in the table above.

Effort of weight on symbol location can be better explained by an example;

635.43 = 6x10² + 3x10¹ + 5x10⁰ + 4x10^-1 + 3x10^-2
              = 600 + 30 + 5 + 0.4 + 0.03
              = 635.43


The principle of positional weight can be exerted to any number system using equation below;
  Y =  (An x rⁿ) + (A_n-1 x r^n-1) +(A₁ x r¹) + (A₀ x r⁰)


Where Y is the value of the entire number, An is the value of the nth digit from the point and r is the radix or base.

MSD & LSD: The left Most System significant digit while the symbol in the rightmost digit is said to be  in the least significant location or LSD.

Example: What are the symbols and weights in the MSD and LSD of the number 7342.084

SOLUTION

MSD symbol = 7, weight 10³
LSD symbol =  4, Weight 10^-3

NEXT TUTORIAL IS THE BINARY NUMBER SYSTEM

[ParadiseAdministrator]

Good one @Hatch

[ChimexLv2: Member]

good one

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