Convert (6806)10 to Binary and (7305)8 to Hexadecimal.
Answers
Your answer is 680616 = 1101000000001102
(6806)10 to Binary is (1101010010110)₂ and (7305)8 to Hexadecimal is (EC5)₁₆.
Steps to convert a number in decimal number system to binary number system.
- The number (decimal) is divided by 2
- Obtained number is written beneath it
- Remainder, 0 or 1, is written sidewise.
- Continue dividing until the number obtained below is 0
- The most significant bit (MSB) is at the bottom of the column of remainders and the least significant bit (LSB) is at the top, i.e. counting of remainders is done from bottom to top.
For (6806)₁₀ , the above steps are followed.
Remainders obtained are 0,1,1,0,1,0,0,1,0,1,0,1,1.
So, the reversed sequence is 1,1,0,1,0,1,0,0,1,0,1,1,0.
Thus the binary number is (1101010010110)₂
To convert octal to hexadecimal, first we convert octal to decimal, and then from decimal to hexadecimal.
Each digit of the octal number is multiplied to its corresponding power of 8.
In 7305, 5 is multiplied with 8⁰. So (5 × 8⁰) = 5
0 is multiplied with 8¹. So, (0 × 8¹) = 0
3 is multiplied with 8². So, (3 × 8²) = 192
7 is multiplied with 8³. So, (7 × 8³) = 3584
Adding them, we get the decimal number = (3584 + 192 + 0 + 5)₁₀ = (3781)₁₀
To convert the decimal to hexadecimal we follow the previous steps, which we did when we converted decimal to binary, the only difference is that we will be dividing 3781 by 16, instead of 2.
Remainders obtained are 5, 12, 14.
The hexadecimal representation of 12 and 14 are C and E respectively.
So, the hexadecimal number is (EC5)₁₆
Thus, (7305)₈ = (EC5)₁₆