CPS 4.01 - Spring, 2002 - Ramm 1/30/02

Binary Arithmetic

• Work with only 2 Digit Values: 0 and 1
  • Two values, thus: binary
  • Binary digit usually called bit

• Addition: Use Same Kinds of Rules a Decimal
  • Carry when sum is too large
  • Start with 0
  • Start adding 1's to get numbers
  • Is like Counting:
  • Can get Binary Number table:

    System:	Binary						Dec
    Weights:	8	4	2	1			10	1
    	0	0	0	0			0	0
    	0	0	0	1			0	1
    	0	0	1	0			0	2
    	0	0	1	1			0	3
    	0	1	0	0			0	4
    	0	1	0	1			0	5
    	0	1	1	0			0	6
    	0	1	1	1			0	7
    	1	0	0	0			0	8
    	1	0	0	1			0	9
    	1	0	1	0			1	0
    	1	0	1	1			1	1
    	1	1	0	0			1	2
    	1	1	0	1			1	3
    	1	1	1	0			1	4
    	1	1	1	1			1	5

• Conversion to and from Decimal
  • To convert to decimal, use weights (as shown in table)
  • To convert to binary, use the successive division method (in text)

• Multiplication and Division by 2
  • Think of what happens in decimal when multiplying (or dividing) by 10
  • Equivalent of binary shift operations

• How Large a Number Can it Hold?
  • One bit can hold 2 different values
  • Two bits can hold 4 different values
  • Three bits can hold ...

• Do We Need Negative Numbers?
  • Most languages allow signed and unsigned integers

• Signed Integers
  • Sign Magnitude System (used in quiz)
    • Easy for beginners
    • Hard on computers
  • Two's Complement System
    • Less intuitive for people
    • Easy on computers