Slide 3.2: Numbering systems Slide 3.4: Integer storage sizes Home

Binary Numbers

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• Translating unsigned decimal integers to binary:
  1. Repeatedly divide the decimal value by 2.
  2. Save each remainder as a binary digit.
  3. Collect the binary digit in the remainder column in reverse order.
  
  

  Integer Division	Quotient	Remainder
  41 / 2		a0 =
  / 2		a1 =
  / 2		a2 =
  / 2		a3 =
  / 2		a4 =
  / 2		a5 =
  Answer: (41)10 = (a5a4a3a2a1a0)2 = ( )2

Binary Addition

1. Proceed bit by bit, beginning with the lowest order pair of bits (on the right side).
2. Each bit triple is added such as (i) 0+0+0=0, (ii) 0+0+1=1, (iii) 1+1+0=10, and (iv) 1+1+1=11. The extra digit generates a carry to the next-highest bit position.
   
   

   Carry
   Augend     (45)10 Addend     (39)10	+		1 1	0 0	1 0	1 1	0 1	1 1
   Sum     (84)10 = ( )2