Which numbering system is based on powers of eight and uses digits 0-7?

Which numbering system is based on powers of eight and uses digits 0-7?

• A. Decimal Numbering System
• B. Octal Numbering System
• C. Binary Numbering System
• D. Hexadecimal Numbering System

Answer: (B)

Base-8 numbering uses digits 0 through 7 and each position represents a power of eight. That means a number written in this system is a sum of digits times eight raised to increasing powers, just like decimal uses powers of ten. For example, the octal number 345 means 3×8^2 + 4×8^1 + 5×8^0, which equals 192 + 32 + 5 = 229 in decimal. Octal is convenient in computing because eight is 2^3, so every octal digit corresponds neatly to a group of three binary digits, making conversions between binary and octal straightforward. This contrasts with decimal, which uses digits 0-9 and powers of ten; binary, which uses digits 0-1 and powers of two; and hexadecimal, which uses digits 0-9 and A-F and powers of sixteen.

Base-8 numbering uses digits 0 through 7 and each position represents a power of eight. That means a number written in this system is a sum of digits times eight raised to increasing powers, just like decimal uses powers of ten. For example, the octal number 345 means 3×8^2 + 4×8^1 + 5×8^0, which equals 192 + 32 + 5 = 229 in decimal. Octal is convenient in computing because eight is 2^3, so every octal digit corresponds neatly to a group of three binary digits, making conversions between binary and octal straightforward. This contrasts with decimal, which uses digits 0-9 and powers of ten; binary, which uses digits 0-1 and powers of two; and hexadecimal, which uses digits 0-9 and A-F and powers of sixteen.