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    cloudiiiday
    Jun 15

    6/6 Computer Number Systems

    in ACSL Contest Prep

    In today’s class, we went over computer number systems, basic operations, and converting between different bases.


    Homework:


    Class Notes:

    Computer Number Systems:

    • The decimal system (base 10) is the number system we commonly use. It uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

    • The binary system (base 2) is commonly used by computers. It uses the digits 0 and 1

    • Octal System (base 8) uses the digits 0, 1, 2, 3, 4, 5, 6, 7

    • Hexadecimal System (base 16) uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. (Since there is not enough digits, A refers to decimal 10, B refers to decimal 11, etc.)

    Operations:

    • When adding or subtracting decimal numbers, you would carry/borrow 10. This means you would carry/borrow 2 for binary, 8 for octal, 16 for hexadecimal

    • Binary multiplication: Binary Multiplication - Exploring Binary

    • Binary division: Binary Division - Exploring Binary

    Converting Between Different Bases:

    • Converting a number to base 10 from another base:

    • Expand the number by place values and compute the value in decimal

    • Ex: 345 (base 8) (38^2)+(48^1)+(5*8^0) = 229 (base 10)

    • Converting a number from base 10 to another base:

    • Write out the powers of the other base starting from the power of 0 to the highest power that does not exceed the given number

    • Divide the given number by the highest power and the quotient will be the leftmost digit of the final answer

    • Keep repeating the steps using the remainder of the division and add on the quotients to the right of your final answer


    1 comment
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    Iris L.
    7d

    13. 58 16. 274 14. 3849 17. 525

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    1 comments

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