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### Grade 6 - Mathematics1.12 Converting Decimal System Into Binary System

Decimal System:
• The system in which ten digits (namely, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are used to describe numbers is called the Decimal System.
• In the decimal system the ten digits written above are called the base digits. Hence the decimal system is Base Ten System.

Example:
Change the binary number 1100 into Decimal System. 11002 = (___)10
Here we use the place value chart of the Binary System. We solve this problem by multiplying each digit with its place value and add the products to get the answer.
11002 = 1x23 + 1x22 + 0x21 + 0x20 = 1x8 + 1x4 + 0x2 + 0x1 = 8 + 4 + 0 + 0= 12

Verification: You can check this answer by changing the answer into Binary System.
 2 12 2 6 0 2 3 0 2 1 1 2 0 1
Therefore (12)10 = (1100)2

Directions: Convert the Base-Two Numerals into Base-Ten Numerals and verify your anwer. Also write at least 10 examples of your own.
 Q 1: 100102 = (___)1019181524 Q 2: 10002 = (___)109864 Q 3: 1100112 = (___)1059none of these5356 Q 4: 1012 = (___)10none of these593 Q 5: 10012 = (___)10191289 Q 6: 1112 = (___)106794 Q 7: 110012 = (___)1025192826 Q 8: 10102 = (___)1011101512 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!