Question

Express each binary number in decimal. $$ 11111111 $$

   Express each binary number in decimal.
$$
11111111
$$

Discrete Mathematics

Discrete Mathematics

Richard Johnsonbaugh 8th Edition

Chapter 5, Problem 15

Instant Answer

Solved by Expert Ahmad Reda

01/27/2023

Step 1

Step 1: First, we need to understand that each digit in a binary number represents a power of 2, starting from 0 at the rightmost digit and increasing by 1 as we move to the left. Show more…

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Express each binary number in decimal. $$ 11111111 $$

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Key Concepts

Binary Numeral System

The binary numeral system is a base-2 numeral system that uses only two symbols, typically 0 and 1, to represent numbers. It is fundamental in the field of computer science and digital electronics because computers use binary digits (bits) to process and store data due to their two-state nature.

Positional Notation

Positional notation is a method of representing or encoding numbers where the position of a digit in a number determines its value. In any numeral system, including binary and decimal, each digit's value is determined by multiplying the digit by a power of the base corresponding to its position.

Binary to Decimal Conversion

Binary to decimal conversion is the process of translating a number from base-2 to base-10. This conversion is accomplished by summing the products of each binary digit (bit) and its corresponding power of 2, which is dictated by its position in the binary sequence.

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