Answered: Convert the following numbers into base…

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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Question

Convert the following numbers into base ten.

(a)

32_five

(b)

22_six

(c)

410_five

(d)

3203_five

(e)

202_five

(f)

1222_six

(g)

202_four

(h)

404_seven

(i)

1000_two

(j)

11011_two

(k)

88_sixteen

(l)

707_{sixteen ?}

Expert Solution

Step 1: Explain general formula for conversion:

To convert numbers from different bases to base ten (decimal), we can use the following method:

For example, to convert a number in base X to base ten, we can use this formula:

Decimal Value $equals a left square bracket n minus 1 right square bracket asterisk times X to the power of left parenthesis n minus 1 right parenthesis end exponent plus a left square bracket n minus 2 right square bracket asterisk times X to the power of left parenthesis n minus 2 right parenthesis end exponent plus... plus a left square bracket 1 right square bracket asterisk times X to the power of 1 plus a left square bracket 0 right square bracket asterisk times X to the power of 0$

Where:

Decimal Value is the equivalent value in base ten.
X is the base of the number.
a[i] represents the digit at position i in the number.
n is the number of digits in the number.

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