let us say the number
127
it is base 10 meaning we have 10 fingers and we based our nums on it
127 is
7 × 10^0 | 7 × 1     | 7
2 × 10^1 | 2 × 10   | 20
1 × 10^2 | 1 × 100 | 100
………………………………………..
.                                    127

similarly our 1001
(1 thousand and 1)
1 × 10^0 | 1 × 1       | 1
0 × 10^1 | 0 × 10     | 0
0 × 10^2 | 0 × 100   | 0
1 × 10^3 | 1 × 1000 | 1000
………………………………………………
.                                      1001

now let us represent binary numbers
the same way
let us say binary 101
it is,

1 × 2^0 | 1 × 1 | 1
0 × 2^1 | 0 × 2 | 0
1 × 2^2 | 1 × 4 | 4
………………………………………..
.                             5

let us try 10010110 in binary
what it represents
it is
0 × 2^0 | 0 × 1     | 0
1 × 2^1 | 1 × 2     | 2
1 × 2^2 | 1 × 4     | 4
0 × 2^3 | 0 × 8     | 0
1 × 2^4 | 1 × 16   | 16
0 × 2^5 | 0 × 32   | 0
0 × 2^6 | 0 × 64   | 0
1 × 2^7 | 0 × 128 | 128
……………………………………………
.                                  150

so we see a pattern
if we have
number (base b)
to get the representation in decimal or decinary we do
sum(digit × b^n)
where digit and n begins from the right most(edited)
so if we were to convert
544 base 16 to base 10, no worry
we do as we did above
rem : sum(digit × b^n)

4 × 16^0 | 4 × 1     | 4
4 × 16^1 | 4 × 16   | 64
5 × 16^2 | 5 × 256 | 1280
…………………………………………………
.                                    1348
that should get us set up with converting other bases to base 10

 

 

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