Sure! Let's break down the conversion of the date "6/21/2024" to binary step by step for each component (month, day, year) and explain the process clearly.
Step 1: Convert Each Component to Decimal
The date provided is "6/21/2024", which consists of:
- Month: 6
- Day: 21
- Year: 2024
Step 2: Convert Month (6) to Binary
To convert the decimal number 6 to binary:
- Start dividing the number by 2 and record the remainder for each division until you reach 0.
Here’s the process for converting 6:
- \(6 \div 2 = 3\) remainder 0 (Least Significant Bit)
- \(3 \div 2 = 1\) remainder 1
- \(1 \div 2 = 0\) remainder 1 (Most Significant Bit)
Now, read the remainders from bottom to top: 110.
Thus, the binary representation of 6 is 110.
Step 3: Convert Day (21) to Binary
For the decimal number 21:
- \(21 \div 2 = 10\) remainder 1
- \(10 \div 2 = 5\) remainder 0
- \(5 \div 2 = 2\) remainder 1
- \(2 \div 2 = 1\) remainder 0
- \(1 \div 2 = 0\) remainder 1
Reading the remainders from bottom to top gives us 10101.
Thus, the binary representation of 21 is 10101.
Step 4: Convert Year (2024) to Binary
For the decimal number 2024:
- \(2024 \div 2 = 1012\) remainder 0
- \(1012 \div 2 = 506\) remainder 0
- \(506 \div 2 = 253\) remainder 0
- \(253 \div 2 = 126\) remainder 1
- \(126 \div 2 = 63\) remainder 0
- \(63 \div 2 = 31\) remainder 1
- \(31 \div 2 = 15\) remainder 1
- \(15 \div 2 = 7\) remainder 1
- \(7 \div 2 = 3\) remainder 1
- \(3 \div 2 = 1\) remainder 1
- \(1 \div 2 = 0\) remainder 1
Reading the remainders from bottom to top gives us 11111100100.
Thus, the binary representation of 2024 is 11111100100.
Step 5: Combine Binary Representations
Now, we can combine the binary representations of the month, day, and year:
- Month (6) in binary: 110
- Day (21) in binary: 10101
- Year (2024) in binary: 11111100100
Optional: Combine All Together
If we want a single binary string that represents the entire date, we can concatenate these binary strings:
Binary Date Representation: 110 (for month) + 10101 (for day) + 11111100100 (for year) = 11010111111100100
Summary
- Month (6) = 110
- Day (21) = 10101
- Year (2024) = 11111100100
- Combined: 11010111111100100
This process shows how we obtained the binary representation for the date "6/21/2024."