1. Chapter 2 Number Systems Consists of a set of symbols called digits and a set of relations such as +, -, x, /.

2. RADIX OR BASE

3. BINARY NUMBER SYSTEM

4. BINARY/DECIMAL

5. OCTAL NUMBER SYSTEM

6. HEXIDECIMAL SYSTEM

7. Integers Binary -> Decimal (1 0 1 1) 2 = ( ( (1 x 2 + 0) x 2 + 1) x 2) + 1 = (1x2 2 + 0x2 + 1) x 2 + 1 = (1x2 3 + 0x2 2 + 1x2) + 1 = 1x2 3 + 0x2 2 + 1x2 1 + 1x2 0 = 1x8 + 0x4 + 1x2 + 1x1 = 8 + 0 + 2 + 1 = 11

8. Integers Base -> Decimal l Result <- Most Significant Digit l Multiply Result by Base and add next digit to right l Repeat step 2 until least significant digit has been added Example: (672) 8 == (442) 10

9. Integers Decimal -> Base l Result <- Decimal Number l Divide Result by Base and save remainder l Result <- Quotient l Repeat step 2 until no more quotients Example: (442) 10 == (672) 8

10. Fractions Decimal -> Base l Result <- Decimal Number l Multiply Result by Base and save whole number l Result <- Fraction l Repeat step 2 until no fractions or significance exceeded Example: (0.62) 10 == (0.4753) 8

11. Fractions Base -> Decimal l Divisor <- Denominator of LSD l Treat Fraction as a whole number (that is, ignore decimal point) and convert l Divide the result by the Divisor of Step 1 Example: (0.4753) 8 == (0.619873) 10