Question

(1000111100001000)2 = ( )16

Answer 1

Answer:

hope it helps you mate!!!

Explanation:

8f0516 = 10001111000001012

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Answer 2

Required Answer:-

Given Number:

• (1000111100001000)₂

To Find:

• The hexadecimal equivalent of the given number.

Solution:

This can be done in two ways.

1. Convert the binary number to its decimal equivalent and then to its hexadecimal equivalent.

Calculating the decimal equivalent of (1000111100001000)₂..

= [(1 * 2¹⁵) + (0 * 2¹⁴) + (0 * 2¹³) + (0 * 2¹²) + (1 * 2¹¹) + (1 * 2¹⁰) + (1 * 2⁹) + (1 * 2⁸) + (0 * 2⁷) + (0 * 2⁶) + (0 * 2⁵) + (0 * 2⁴) + (1 * 2³) + (0 * 2²) + (0 * 2¹) + (0 * 2⁰)]₁₀

= (2¹⁵ + 2¹¹ + 2¹⁰ + 2⁹ + 2⁸ + 2³)₁₀

= (32768 + 2048 + 1024 + 512 + 256 + 8)₁₀

= (36616)₁₀

Calculating the hexadecimal equivalent of (36616)₁₀..

$\boxed{\begin{array}{c|c|c}\sf\underline{16}&\sf\underline{36616}&\underline{\ }\\ \sf\underline{16}&\sf\underline{2288}&\sf\underline{8}\\ \sf\underline{16}&\sf\underline{143}&\sf\underline{0}\\ \sf\underline{16}&\sf\underline{8}&\sf\underline{F}\\ &\sf0&\sf8\end{array}}$

Now, write the remainders obtained from bottom to top..

>> (36616)₁₀ = (8F08)₁₆

>> (1000111100001000)₂ = (8F08)₁₆  (Answer)

Note: The following numbers in hexadecimal number system has different names.

$\boxed{\begin{array}{c|c}\tt \underline{Number}:&\tt \underline{Value}:\\ \sf10&\sf A\\ \sf11&\sf B\\ \sf12&\sf C\\ \sf13&\sf D \\ \sf14&\sf E\\ \sf15&\sf F\end{array}}$

2. Using grouping method.

Binary Number = (1000111100001000)₂

On Grouping, we get,

$= \boxed{\sf1000\ |\ 1111\ |\ 0000\ |\ 1000}$

Now, look at the table given below,

$\boxed{\begin{array}{c|c}\tt \underline{HEXA}:&\tt \underline{BINARY}:\\ \sf0&\sf0000\\ \sf1&\sf0001\\ \sf2&\sf0010\\ \sf3&\sf0011\\ \sf4&\sf0100\\ \sf5&\sf0101\\ \sf6&\sf0110\\ \sf7&\sf0111\\ \sf8&\sf1000\\ \sf9&\sf1001\\ \sf A&\sf1010\\ \sf B&\sf1011\\ \sf C&\sf1100\\ \sf D&\sf1101\\ \sf E&\sf1110\\ \sf F&\sf1111\end{array}}$

Substituting the values from here, we get,

= (8F08)₁₆

>> (1000111100001000)₂ = (8F08)₁₆ (Answer)

Answer:

• (1000111100001000)₂ = (8F08)₁₆

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