### 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*10

^{2}represents 3 times base 10 to the exponent 2.

(1234)

_{10}

= 1*10

^{3}+ 2*10

^{2}+ 3*10

^{1}+ 4*10

^{0}

= 1000 + 200 + 30 + 4

= 1234

_{10}

= 1234 the original base 10 number

(1101)

_{2}

= 1*2

^{3}+ 1*2

^{2}+ 0*2

^{1}+ 1*2

^{0}

= 8 + 4 + 0 + 1

= 13

_{10}

= 13 its base 10 number equivalent

(1010)

_{2}

= 1*2

^{3}+ 0*2

^{2}+ 1*2

^{1}+ 0*2

^{0}

= 8 + 0 + 2 + 0

= 10

_{10}

= 10 its base 10 number equivalent

Contributed by

^{www.}TheMathWebSite

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