Decimal to Hexadecimal Conversion

 

Computer Organization | Number System | GATE Preparation

How to Convert 262144 Decimal to 40000 Hexadecimal?

Learn how to convert decimal numbers into hexadecimal numbers using the repeated division-by-16 method. This tutorial explains the conversion of 262144 decimal into 40000 hexadecimal with step-by-step calculations, a division table, verification and shortcut techniques for GATE Computer Science examinations.

Number System Conversion

Question: Convert Decimal to Hexadecimal

Convert the decimal number 262144 into its equivalent hexadecimal number.

Given Decimal Number

262144₁₀

1. Understand the Hexadecimal Number System

The hexadecimal number system is a base-16 number system. It uses 16 symbols, starting from 0 to 9 and A to F.

Decimal	Hexadecimal
0 to 9	0 to 9
10	A
11	B
12	C
13	D
14	E
15	F

2. Divide the Decimal Number by 16

To convert a decimal number into hexadecimal, repeatedly divide the number by 16 and note the remainder at each step.

Division Method

\[ \text{Quotient} = \frac{\text{Number}}{16} \] \[ \text{Remainder} = \text{Number} \bmod 16 \]

Step-by-Step Division Table

Step	Division	Quotient	Remainder
1	262144 ÷ 16	16384	0
2	16384 ÷ 16	1024	0
3	1024 ÷ 16	64	0
4	64 ÷ 16	4	0
5	4 ÷ 16	0	4

Important Rule

Continue dividing until the quotient becomes zero. Then write all the remainders from bottom to top.

3. Write the Remainders from Bottom to Top

From the division table, the remainders are:

4 0 0 0 0

Read from bottom to top

\[ 262144_{10}=40000_{16} \]

Final Answer

Decimal to Hexadecimal Conversion

\[ \boxed{262144_{10}=40000_{16}} \]

Therefore, 262144 decimal is equal to 40000 hexadecimal.

4. Verify the Answer: Hexadecimal to Decimal

We can verify the result by converting 40000 hexadecimal back into decimal.

\[ 40000_{16} \] \[ =4\times16^4+0\times16^3 \] \[ +0\times16^2+0\times16^1+0 \] \[ =4\times65536 \] \[ =262144_{10} \]

✓ The conversion is correct!

5. Shortcut Method for GATE Exams

For faster calculations, remember these useful decimal-to-hexadecimal values:

Decimal	Hexadecimal
16	10H
256	100H
1024	400H
4096	1000H
65536	10000H
262144	40000H

Shortcut Calculation

\[ 262144=256\times1024 \] Since: \[ 256=100_H \] \[ 1024=400_H \] Therefore: \[ 100_H\times400_H =40000_H \]

This shortcut is particularly useful for memory size and address calculation questions.

Summary

• ✓ Hexadecimal is a base-16 number system.
• ✓ Always divide by 16 when using the repeated division method.
• ✓ Write the remainders from bottom to top.
• ✓ Remember that A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.
• ✓ Verify your answer by converting hexadecimal back into decimal.

Frequently Asked Questions

How do you convert decimal to hexadecimal?

Repeatedly divide the decimal number by 16. Write the remainders from bottom to top to obtain the hexadecimal equivalent.

What is 262144 in hexadecimal?

262144 in decimal is equal to 40000 in hexadecimal.

Why do we divide by 16 in hexadecimal conversion?

Because hexadecimal is a base-16 number system. Therefore, repeated division by 16 gives the hexadecimal digits as remainders.

What is the difference between decimal and hexadecimal?

Decimal uses base 10 with digits 0 to 9, whereas hexadecimal uses base 16 with digits 0 to 9 and A to F.

Conclusion

Decimal-to-hexadecimal conversion is an important concept in Computer Organization and Architecture. By using repeated division by 16, we can easily convert 262144 decimal into 40000 hexadecimal. Understanding this technique helps solve GATE questions involving memory addressing, memory size and number systems.