Binary Numbers

Binary numbers are written with two symbols 0 & 1.
Decimal numbers use the ten symbols 0,1,2,...8,9.
To represent numbers,
the decimal system uses the
powers of base 10 to an exponent,
the binary system uses
the powers of base 2 to an exponent.

(3274)₁₀ represents the base 10 number 3274.
(1001)₂ represents the base 2 number 1001.
3*10² represents 3 times base 10 to the exponent 2.

(1234)₁₀
= 1*10³ + 2*10² + 3*10¹ + 4*10⁰
= 1000 + 200 + 30 + 4
= 1234₁₀
= 1234 the original base 10 number

(1101)₂
= 1*2³+ 1*2² + 0*2¹ + 1*2⁰
= 8 + 4 + 0 + 1
= 13₁₀
= 13 its base 10 number equivalent

(1010)₂
= 1*2³+ 0*2² + 1*2¹ + 0*2⁰
= 8 + 0 + 2 + 0
= 10₁₀
= 10 its base 10 number equivalent

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