D. From binary to octal
1. 01110
2. 1000111
3. 1110001

To convert binary numbers to octal numbers, follow these steps:

Understand the relationship between binary and octal:

Each octal digit corresponds exactly to three binary digits (bits). This is because octal (base 8) and binary (base 2) are directly related.


Group the binary digits into sets of three, starting from the right:

If the number of binary digits isn’t a multiple of 3, you can pad the left side with zeros until you have a complete group.


Convert each binary group to an octal digit:

Use the following binary to octal conversions:
000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7





Let's apply these steps to each given binary number:

Binary: 01110

Pad with zero to make full groups: 001 110
Convert each group:
001 = 1
110 = 6


Octal result: 16


Binary: 1000111

Pad with zeros if needed: 001 000 111
Convert each group:
001 = 1
000 = 0
111 = 7


Octal result: 107


Binary: 1110001

Pad with zeros if needed: 001 110 001
Convert each group:
001 = 1
110 = 6
001 = 1


Octal result: 161



The conversion from binary to octal simplifies complex computer operations, making number handling more efficient in computing systems.

Answered by SophiaElizab | 2025-07-21

To convert binary to octal, group the binary digits in sets of three from the right, adding leading zeros if necessary, and then convert each group using the binary-to-octal correspondence. The conversions for the given numbers are: 01110 = 16, 1000111 = 107, and 1110001 = 161. This process greatly aids in efficient number handling in computing.
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Answered by SophiaElizab | 2025-07-23