To convert the binary number $1001001$ to both octal and hexadecimal, let me show the work step by step:

Conversion to Octal

1. Group the binary digits into sets of three starting from the right (add leading zeros if necessary): $001 \, 001 \, 001$

2. Convert each group to its decimal (octal) equivalent:

   • $001$ = $1$ (decimal)
   • $001$ = $1$ (decimal)
   • $001$ = $1$ (decimal)

3. Combine the results: $1001001_2 = 111_8$

Conversion to Hexadecimal

1. Group the binary digits into sets of four starting from the right (add leading zeros if necessary): $0001 \, 0010 \, 001$ Add a leading zero to complete the last group: $0001 \, 0010 \, 0001$

2. Convert each group to its decimal (hexadecimal) equivalent:

   • $0001$ = $1$ (hexadecimal)
   • $0010$ = $2$ (hexadecimal)
   • $0001$ = $1$ (hexadecimal)

3. Combine the results: $1001001_2 = 49_{16}$

Final Answer:

• Octal: $111_8$
• Hexadecimal: $49_{16}$

Would you like further clarification or details on any step?

Related Questions:

1. How can binary numbers be directly converted to decimal?
2. What is the difference between octal and hexadecimal systems in terms of digit grouping?
3. Can we convert $1001001$ directly to decimal and back to octal/hexadecimal?
4. What are some practical applications of octal and hexadecimal conversions?
5. Why is binary grouping essential when converting to octal or hexadecimal?

Tip:

Always ensure to group binary digits correctly to avoid errors in conversions!