Use the place value method, the division method, or the equivalency chart to convert the following....

Use the place value method, the division method, or the equivalency chart to convert the following. You must show all steps.

Convert the following decimal numbers to the binary number system. a. 10 b. 43 c. 96 d. 156 e. 255

Solutions

Expert Solution

a) 10
Divide 10 successively by 2 until the quotient is 0
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1010
So, 10 of decimal is 1010 in binary
Answer: 00001010

b) 43
Divide 43 successively by 2 until the quotient is 0
   > 43/2 = 21, remainder is 1
   > 21/2 = 10, remainder is 1
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 101011
So, 43 of decimal is 101011 in binary
Answer: 00101011

c) 96
Divide 96 successively by 2 until the quotient is 0
   > 96/2 = 48, remainder is 0
   > 48/2 = 24, remainder is 0
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100000
So, 96 of decimal is 1100000 in binary
Answer: 01100000

d) 156
Divide 156 successively by 2 until the quotient is 0
   > 156/2 = 78, remainder is 0
   > 78/2 = 39, remainder is 0
   > 39/2 = 19, remainder is 1
   > 19/2 = 9, remainder is 1
   > 9/2 = 4, remainder is 1
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10011100
So, 156 of decimal is 10011100 in binary
Answer: 10011100

e) 255
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
Answer: 11111111

venereology answered 9 months ago

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