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### Grade 6 - Mathematics1.11 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 =
 102 101 10 2 3 4 2x102 3x101 4x100 200 30 4
The number is 234
Example: 101 that is (101)2 =
 22 21 20 1 0 1 1x22 0x21 1x20 4x1 2x0 1x1
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: 8110 = (_______)2none of these101000110101011001001 Q 2: (51)10 = (_______)2110101100111101111011 Q 3: 2510 = (_______)21100111100none of these10101 Q 4: 100110 = (_______)21010111010101010111111010011111000011 Q 5: 121010 = (_______)210001001011001011101010101110011010101111 Q 6: 3610 = (_______)2100100101010111000110011 Q 7: 910 = (_______)21001111010101100 Q 8: 144110 = (_______)210101101010111000111001011010110none of these Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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