Introduction to definition of base in math:
In arithmetic, the radix or base refers the number b in an expression of form bn. The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power". (Source: Wikipedia).
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Examples for definition of base in math:
Example 1 for definition of base in math:
Find the base 2 for base 10 of 28.
Solution:
The given base 2 number is (28)10.
We have to convert the base 10 number to base 2 numbers that is in the binary format.
The binary representation for the number 2 is 0010 and the binary representation for the number 8 is 1000. For 28 the binary value is 0010 1000.
So the value of base 10 for the number (28)10 is (0010 1000)2.
Example 2 for definition of base in math:
Find the base 10 for (1111)2.
Solution:
The given base 2 value is (1111)2.
The binary value for 15 is 1111 using the 8 4 2 1 method.
So the decimal value for the (1111)2 is 15.
Example 3 for definition of base in math:
Convert the base 2 value 11010101 into base 6 of the hexadecimal.
Solution:
The given base 2 value is 11010101.
Separate the binary values as 4 digits.
11010101 = 1101 0101
The hexadecimal values are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D. . . . . . So,
11010101 = D 5
The hexadecimal value for 11010101 is D5.
Example 4 for definition of base in math:
Convert the base 2 value 10011011 into base 6 of the hexadecimal.
Solution:
The given base 2 value is 10011011.
Separate the binary values as 4 digits.
10011011 = 1001 1011
The hexadecimal values are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D. . . . . . So,
11010101 = 9 B
The hexadecimal value for 11010101 is 9B.
Practice problem for definition of base in math:
Convert the (1110)2 into the decimal number.
Answer: 14
Convert 43 into the binary number.
Answer: 01000011
Convert the 10111010 into hexadecimal number.
Answer: B A.
In arithmetic, the radix or base refers the number b in an expression of form bn. The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power". (Source: Wikipedia).
Please express your views of this topic Hexadecimal to Binary by commenting on blog.
Examples for definition of base in math:
Example 1 for definition of base in math:
Find the base 2 for base 10 of 28.
Solution:
The given base 2 number is (28)10.
We have to convert the base 10 number to base 2 numbers that is in the binary format.
The binary representation for the number 2 is 0010 and the binary representation for the number 8 is 1000. For 28 the binary value is 0010 1000.
So the value of base 10 for the number (28)10 is (0010 1000)2.
Example 2 for definition of base in math:
Find the base 10 for (1111)2.
Solution:
The given base 2 value is (1111)2.
The binary value for 15 is 1111 using the 8 4 2 1 method.
So the decimal value for the (1111)2 is 15.
Example 3 for definition of base in math:
Convert the base 2 value 11010101 into base 6 of the hexadecimal.
Solution:
The given base 2 value is 11010101.
Separate the binary values as 4 digits.
11010101 = 1101 0101
The hexadecimal values are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D. . . . . . So,
11010101 = D 5
The hexadecimal value for 11010101 is D5.
Example 4 for definition of base in math:
Convert the base 2 value 10011011 into base 6 of the hexadecimal.
Solution:
The given base 2 value is 10011011.
Separate the binary values as 4 digits.
10011011 = 1001 1011
The hexadecimal values are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D. . . . . . So,
11010101 = 9 B
The hexadecimal value for 11010101 is 9B.
Practice problem for definition of base in math:
Convert the (1110)2 into the decimal number.
Answer: 14
Convert 43 into the binary number.
Answer: 01000011
Convert the 10111010 into hexadecimal number.
Answer: B A.
