Certainly! Let's convert each of the given octal numbers to binary step-by-step:
(A) 472 (octal) to binary:
1. Start by converting each digit of the octal number to its 3-bit binary equivalent.
- 4 (octal) = 100 (binary)
- 7 (octal) = 111 (binary)
- 2 (octal) = 010 (binary)
2. Combine these binary groups together:
- 472 (octal) = 100 111 010 (binary)
3. Remove any leading zeros:
- 472 (octal) = 100111010 (binary)
(B) 145 (octal) to binary:
1. Convert each digit of the octal number to its 3-bit binary equivalent:
- 1 (octal) = 001 (binary)
- 4 (octal) = 100 (binary)
- 5 (octal) = 101 (binary)
2. Combine these binary groups together:
- 145 (octal) = 001 100 101 (binary)
3. Remove any leading zeros:
- 145 (octal) = 1100101 (binary)
(C) 347 (octal) to binary:
1. Convert each digit of the octal number to its 3-bit binary equivalent:
- 3 (octal) = 011 (binary)
- 4 (octal) = 100 (binary)
- 7 (octal) = 111 (binary)
2. Combine these binary groups together:
- 347 (octal) = 011 100 111 (binary)
3. Remove any leading zeros:
- 347 (octal) = 11100111 (binary)
(D) 6247 (octal) to binary:
1. Convert each digit of the octal number to its 3-bit binary equivalent:
- 6 (octal) = 110 (binary)
- 2 (octal) = 010 (binary)
- 4 (octal) = 100 (binary)
- 7 (octal) = 111 (binary)
2. Combine these binary groups together:
- 6247 (octal) = 110 010 100 111 (binary)
3. Remove any leading zeros:
- 6247 (octal) = 110010100111 (binary)
(E) 645 (octal) to binary:
1. Convert each digit of the octal number to its 3-bit binary equivalent:
- 6 (octal) = 110 (binary)
- 4 (octal) = 100 (binary)
- 5 (octal) = 101 (binary)
2. Combine these binary groups together:
- 645 (octal) = 110 100 101 (binary)
3. Remove any leading zeros:
- 645 (octal) = 110100101 (binary)
So the binary equivalents of the given octal numbers are:
(A) 472 (octal) = 100111010 (binary)
(B) 145 (octal) = 1100101 (binary)
(C) 347 (octal) = 11100111 (binary)
(D) 6247 (octal) = 110010100111 (binary)
(E) 645 (octal) = 110100101 (binary)
