Find the hexadecimal expansion of (12345)10
The Correct Answer and Explanation is:
To find the hexadecimal (base 16) expansion of the decimal number 12345, we convert it by repeatedly dividing by 16 and recording the remainders.
Step-by-step conversion:
- 12345 ÷ 16 = 771 remainder 9
- 771 ÷ 16 = 48 remainder 3
- 48 ÷ 16 = 3 remainder 0
- 3 ÷ 16 = 0 remainder 3
Now, we take the remainders from last to first: 3 0 3 9
Therefore, the hexadecimal expansion of 12345 is 0x3039
Final Answer:
(12345)₁₀ = (3039)₁₆
Explanation:
The hexadecimal number system uses base 16. It has sixteen digits: 0 to 9 and then A to F. The letters A to F represent decimal values 10 to 15. For example, A equals 10, B equals 11, and so on up to F which equals 15. This system is widely used in computing because it is more compact than binary and maps easily to it.
To convert a decimal number to hexadecimal, we divide the number repeatedly by 16 and keep track of the remainders. Each remainder corresponds to a hexadecimal digit. The process stops when the quotient reaches zero. The hexadecimal number is read from the last remainder to the first.
In this case, dividing 12345 repeatedly by 16 gave us remainders 9, 3, 0, and 3 in that order. Reversing this list gives us the hexadecimal digits 3, 0, 3, 9. Hence, 12345 in decimal is equal to 3039 in hexadecimal.
Hexadecimal numbers are often used in programming and digital electronics because they are more human-friendly than binary. For example, memory addresses, color codes in HTML and CSS, and machine code instructions often use hexadecimal notation.
