Answer to Question #226036 in Combinatorics | Number Theory for Minenhle Pelican C

Question

Demonstrate how you add the numbers 111_2, 110_2, 1100_2, 101_2, and 1111_2.  Check your answer by calculating the decimal numbers for the above.

Answer 1

We need to add :

(111)₂ + (110)₂ + (1100)₂ + (101)₂ + (1111)₂

Step 1:

1 1 1

1 1 0

---------------

1 1 0 1

---------------

Step 2: Now Add

(1101)₂ + (1100)₂

1 1 0 1

1 1 0 0

--------------------

1 1 0 0 1

---------------------

Step 3: Now Add

(11001)₂ + (101)₂

1 1 0 0 1

1 0 1

---------------------

1 1 1 1 0

---------------------

Step 4: Now Add

(11110)₂ + (1111)₂

1 1 1 1 0

1 1 1 1

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1 0 1 1 0 1 ------------------------------- (1)

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Checking the answer

Now convert the decimals into Binary equivalent.

(111 )₂ = 7

(110)₂ = 6

(1100)₂ = 12

(101)₂ = 5

(1111)₂ = 15

Sum =7 + 6 +12 +5 +15

Sum = 45

(45)₁₀ =(101101)₂ Which is equal to equation (1)