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NUMBER BASE CONVERSION, photo_2023-08-02_16-17-19, photo_2023-08-02_15-59…
NUMBER BASE CONVERSION
BINARY
Base "2" : 0,1
Example : 512.74, Base 2 -> Base 10
Sollution = (5x2^2) + (1x2^1) + (2x2^0) + (7x2^-1) + (4x2^-2)
The answer getting smaller it is because base 2 is smaller than base 10.
DECIMAL
Base "10" : 0,1,2,3,4,5,6,7,8,9
Example : 512.74, Base 10
The answer is same because the calculator using "DEC" system.
Sollution : (5x10^2) + (1x10^1) + (2x10^0) + (7x10^-1) + (4x10^-2)
OCTAL
Example : 512.74, Base 8 -> Base 10
Sollution : (5x10^2) + (1x10^1) + (2x10^0) + (7x10^-1) + (4x10^-2)
Base "8" : 0,1,2,3,4,5,6,7
The answer getting smaller because the base 8 is smaller than the base 10
HEXADECIMAL
Base "16" : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
Example : 512.74, Base 16 -> Base 10
Sollution : (5x10^2) + (1x10^1) + (2x10^0) + (7x10^-1) + (4x10^-2)
The answer getting bigger because the base 16 is bigger than the base 10
DECIMAL -> BINARY
INTEGER
Example : 13 , Base 10
13/2 = 6 -> 1 6/2 = 3 -> 0 3/2 = 1 -> 1 1/2 = 0 -> 1
Answer = 1101, Base 2#
FRACTION
Example : 0.625 , Base 10
0.625 2 = 1 .25 0.25 2 = 0.5
0.5 * 2 = 1.0
Answer = 0.101, Base 2#
DECIMAL -> OCTAL
175/8 = 21 -> 7 21/8 = 2 -> 5 2/8 = 0 -> 2
Answer = 257, Base 8#
Example : 175 , Base 10
BINARY -> OCTAL
Example : 10110.01
BINARY > HEXADECIMAL
Example : 10110.01, Base 2
OCTAL > HEXADECIMAL
Example : 26.2, Base 8
Convert to Binary as an intermediate step
Arrow = Assume "0"
