Numbers in Bases Two, Eight and Five (Part 4)

(F) Addition and Subtraction of Two Numbers in Base Two
1. In the addition of two numbers in base two, the following rules applied:
 
  0+ 0= 02
  0+ 1= 12
  1+ 0= 12
  1+ 1= 102
  1+ 1+ 1= 10+ 1= 112
 
2. In the subtraction of two numbers in base two, the following rules applied:
 
  0– 0= 02
  1– 0= 12
  1– 1= 02
  10– 1= 12
   

Example 2:
 
Find the value of each of the following:
(a) 11012 + 1102
(b) 110012 + 101002
(c) 110112 – 11012
(d) 10002 – 1012
 
Solution:
(a)

(b)


(c) 



(d)



Calculator Computation
You may obtain the answer directly from a scientific calculator by pressing:
    [MODE]   [MODE]   [3 (BASE)]
Key in the following:
(a)
[ BIN ] 1101 [ + ] 110 [ = ] 
The screen display is: [ 10011 ]
(b)
[ BIN ] 11001 [ + ] 11100 [ = ] 
The screen display is: [ 110101 ]
(c)
[ BIN ] 11011  ] 1101 [ = ] 
The screen display is: [ 1110 ]
(d)
[ BIN ] 1000  ] 101 [ = ] 
The screen display is: [ 11 ]

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