6/6 Computer Number Systems

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