Final answer:
The 16-bit binary pattern for the decimal number 6 is 0000 0000 0000 0110. To arrive at this, divide the number by 2 and note the remainders. The binary number reads from the last remainder back to the first, padded with zeros to fit the 16-bit format.
Step-by-step explanation:
The binary pattern that represents 6 in a 16-bit binary system is 0000 0000 0000 0110. To convert the decimal number 6 to binary, we divide the number by 2 and write down the remainder. We continue this process with the quotient until we reach 0.
The binary number is formed by reading the remainders backwards (from the last division to the first). In a 16-bit binary system, we simply add zeros in front of the result to fill up the remaining bits.
Here's the step-by-step division process:
- 6 ÷ 2 = 3 with remainder 0
- 3 ÷ 2 = 1 with remainder 1
- 1 ÷ 2 = 0 with remainder 1
Reading the remainders backwards gives us 110. Adding the additional zeros for a 16-bit system gives us:
0000 0000 0000 0110