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Online Quiz (Worksheet A B C D)

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Grade 6 - Mathematics
1.11 Converting Binary System Into Decimal System

Decimal SystemBinary System
Base ten systemBase two system
0,1,2,3,4,5,6,7,8,90,1
Example: 234 that is (234)2 =
10210110
234
2x1023x1014x100
200304
The number is 234
Example: 101 that is (101)2 =
222120
101
1x220x211x20
4x12x01x1
The number is 4+1 = 5
Binary System:
Two digits "0" and "1" are used for computation in computers. This system is called Binary System (or the base-two system) as the base digits are only two.

Table: Place value chart for Binary System
1 1Unit's Place
2 2 Two's Place
22 4 Four's Place
23 8Eight's Place
24 16Sixteen's Place
25 32Thirty two's Place
26 64 Sixty Four's Place
27 128 One Hundred Twenty Eight's Place
Method:
  • Divide the number by 2. If it is divisible by 2, write 0. If not write 1.
  • Take the quotient
  • Divide the quotient by 2. If it is divisible by 2, write 0. If not write 1.
  • Take the quotient and divide by 2
  • Continue this process, until the number which we are left to divide by is 0.
Example:
Change (56)10 Into (______)2.
2 56
2 28 0 Unit's Place
2 140 Two's Place
2 7 0 Four's Place
2 3 1 Eight's Place
2 11 Sixteen's Place
2 0 1 Thirty Two's Place

The answer is third column from down to up, that is 111000 base two that is (111000)2. This is read as one-one-one-zero-zero-zero base two.


Directions: Change the Base Ten Numerals into Base Two Numerals. Also write at least 10 examples of your own.
Q 1: 4910 = (_______)2
11100
10101
10110
110001

Q 2: 910 = (_______)2
1100
1010
1001
1110

Q 3: (51)10 = (_______)2
11011
110011
11010
11011

Q 4: 8110 = (_______)2
1001001
1010101
none of these
1010001

Q 5: 2510 = (_______)2
10101
11100
11001
none of these

Q 6: 100110 = (_______)2
10101110
1111000011
1111101001
101010101

Q 7: 144110 = (_______)2
10101101010
1011010110
none of these
11100011100

Q 8: 121010 = (_______)2
10010111010
1010111001
1000100101
1010101111

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Question 10: This question is available to subscribers only!


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