To express a year in binary form, we first need to convert that year from decimal (base 10) to binary (base 2). For this example, let's use the year 1990 as the significant year.
Steps to Convert 1990 to Binary:
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Divide by 2 and Record the Remainder: Begin by dividing 1990 by 2 and noting the quotient and the remainder. Keep dividing the quotient by 2 until you reach a quotient of 0.
- 1990 ÷ 2 = 995, remainder 0
- 995 ÷ 2 = 497, remainder 1
- 497 ÷ 2 = 248, remainder 1
- 248 ÷ 2 = 124, remainder 0
- 124 ÷ 2 = 62, remainder 0
- 62 ÷ 2 = 31, remainder 0
- 31 ÷ 2 = 15, remainder 1
- 15 ÷ 2 = 7, remainder 1
- 7 ÷ 2 = 3, remainder 1
- 3 ÷ 2 = 1, remainder 1
- 1 ÷ 2 = 0, remainder 1
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Write the Remainders in Reverse Order: Now, take the remainders from the bottom up to form the binary representation.
The remainders collected, starting from the last division to the first, are:
1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0So in reverse order, we have: 11111000110.
Binary Representation:
Thus, the year 1990 in binary form is represented as 11111000110.
Summary:
To summarize, I arrived at the binary representation of the year 1990 by repeatedly dividing the number by 2 and tracking the remainders, ultimately reading these remainders from bottom to top to form the complete binary string. Each digit in this binary form represents a power of 2, where each '1' indicates the presence of that power of 2 in the sum that equals the original decimal number.
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