Suppose that a program performs an intermixed sequence of (stack) push and pop operations. The push operations put the integers
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(10101)_2=(21)10
Given : Number (10101)_2(10101)2
To find : What is the value of (10101)_2(10101)2 in decimal number system?
Solution :
Decimal number system is a positional numeral system employing 10 as the base.
Now, to convert it into base 10
Multiply each digit of the following binary by the corresponding power of 2:
(10101)_2(10101)2
=1\times 2^4+0\times 2^3+1\times 2^2+0\times 2^1+1\times 2^0=1×24+0×23+1×22+0×21+1×20
=1\times 16+0\times 8+1\times 4+0\times 2+1\times 1=1×16+0×8+1×4+0×2+1×1
=16+0+4+0+1=16+0+4+0+1
=21=21
Therefore, (10101)_2=(21)_{10}(10101)2=(21)10