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**FIRST**

I read from John H. Mathews’ Numerical Methods using MATLAB, 3E that the number

1563 can be expanded in form of 10-base expansion as:

(1 × 10[tex]^{3}[/tex]) − (5 × 10[tex]^{2}[/tex]) + (6 × 10[tex]^{1}[/tex]) + (3 × 10[tex]^{0}[/tex]) …...............................................

**(1)**

Which results 1000 − 500 + 60 + 3 equal to 563.

But the number 1563 should be expanded in form of 10-base expansion as:

1563 = 1000 + 500 + 60 + 3

Which means:

(1 × 10[tex]^{3}[/tex]) + (5 × 10[tex]^{2}[/tex]) + (6 × 10[tex]^{1}[/tex]) + (3 × 10[tex]^{0}[/tex]) …...............................................

**(2)**

Hence, (1) ≠ (2) or 1563 ≠ 563.

So, can anyone explain me about these?

**SECOND**

If the number 1563 is expressible in expanded form of 10-base expansion as:

1563 = 1000 + 500 + 60 + 3

=(1 × 10[tex]^{3}[/tex]) − (5 × 10[tex]^{2}[/tex]) + (6 × 10[tex]^{1}[/tex]) + (3 × 10[tex]^{0}[/tex])

how can I express the number 1563 in expanded form of 2-base expansion?

Please advance