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) (3

*8^2)+(4*8^1)+(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

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