Convert the binary expansion of each of these integers to an octal expansion. a) (11110111)2 b)

step 1 So we're asked to write base 8 representation of these numbers. So we're converting them from ba

Convert the binary expansion of each of these integers to an...

Key Concepts

Positional Notation

Positional notation is a method of representing numbers where the position of each digit within a number determines its value relative to the base. Both binary and octal numeral systems use positional notation, with each position representing a power of the base (2 for binary and 8 for octal).

Base Conversion

Base conversion is the process of converting numbers from one numeral system (or base) to another. When converting between numeral systems, the value of each digit is weighted by its position, and the goal is to represent the same numerical value in a different base.

Grouping of Digits for Conversion

A key technique in converting binary numbers to octal is to group the binary digits into sets of three, starting from the right. Since 2^3 equals 8, each group of three binary digits corresponds directly to one octal digit, making the conversion process straightforward and systematic.

Binary Numeral System

The binary numeral system is a base-2 numeral system that uses just two symbols, typically 0 and 1, to represent numbers. Each digit in a binary number represents an increasing power of 2, from right to left. It forms the basis for digital computing since computers operate using binary logic.

Octal Numeral System

The octal numeral system is a base-8 numeral system that uses the digits 0 to 7 to represent numbers. In octal, each digit represents a power of 8, and it is often used in computing as a more compact representation of binary numbers.

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