For question 1, part (a), we are tasked with converting the binary number $1101111101110112$ to both octal and hexadecimal forms.

Conversion to Octal:

To convert the binary number to octal, group the binary digits into sets of three (starting from the right). Add leading zeros if necessary to make complete groups of three:

$1101111101110112 \to 001 101 111 101 110$

Now, convert each group of three binary digits into its octal equivalent:

$001_2 = 1_8, \quad 101_2 = 5_8, \quad 111_2 = 7_8, \quad 101_2 = 5_8, \quad 110_2 = 6_8$

So, the octal equivalent of $1101111101110112$ is $15756_8$.

Conversion to Hexadecimal:

For hexadecimal, group the binary digits into sets of four (starting from the right). Add leading zeros if necessary to complete the groups:

$1101111101110112 \to 0001 1011 1110 1110$

Now, convert each group of four binary digits into its hexadecimal equivalent:

$0001_2 = 1_{16}, \quad 1011_2 = B_{16}, \quad 1110_2 = E_{16}, \quad 1110_2 = E_{16}$

So, the hexadecimal equivalent of $1101111101110112$ is $1BEE_{16}$.

Thus:

• The octal representation is $15756_8$.
• The hexadecimal representation is $1BEE_{16}$.

Let me know if you'd like more details or have any questions!

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Here are some related questions you might find useful:

1. How do you convert from octal to binary?
2. What is the process of converting hexadecimal to binary?
3. Can you explain how to handle signed numbers in binary?
4. What is the difference between binary, octal, and hexadecimal number systems?
5. How do you convert decimal numbers into binary?

Tip: Always group your binary digits in sets of 3 or 4 for octal and hexadecimal conversions, as this will make the process much faster and less error-prone!