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Binary System 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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