What is (1 1101 11012) converted to decimal?

Answered: What is (1 1101 11012) converted to…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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What is (1 1101 1101₂) converted to decimal?

Expert Solution

Explanation

1) (1 1101 1101) is a binary number and can be converted to decimal by computing the sum of the powers of 2 corresponding to the set bits in the binary representation.

2) For binary number with n digits: d_n-1 ... d₃ d₂ d₁ d_0.The decimal number is equal to the sum of binary digits (d_n) times their power of 2 (2ⁿ):

decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + ...

3) (111011101)₂ = (1 × 2⁸) + (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = (477)₁₀

4) So (111011101)₂ in binary is equal to 417 in decimal.

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