Unlock the Power of Conversion with Binary and Hexadecimal
What are the essential steps to convert between decimal, binary, and hexadecimal numbers?
Have you ever wondered about the magic behind decimal, binary, and hexadecimal conversions? Let's explore the steps and unravel the mystery of number transformations.
Steps for Conversion:
To convert decimal to binary, divide by 2 repeatedly until the quotient becomes 0. The remainders form the binary representation.
To convert binary to decimal, multiply each digit by the appropriate power of 2 and sum the results.
To convert binary to hexadecimal, group binary digits into sets of 4 and convert each group to its equivalent hexadecimal digit.
Understanding number conversions is like decoding secret messages in the digital world. Let's delve into each step to unlock the power of conversion:
Decimal to Binary Conversion:
When converting a decimal number to binary, the key is to divide the decimal number by 2 repeatedly. The remainders obtained from each division will give you the binary representation of the number. For example, when converting 255 to binary:
255 ÷ 2 = 127 remainder 1
127 ÷ 2 = 63 remainder 1
63 ÷ 2 = 31 remainder 1
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top, we get the binary representation of 255 as 11111111.
Binary to Decimal Conversion:
Converting a binary number to decimal involves multiplying each digit of the binary number by powers of 2 and then summing up the results. For example, when converting 11101000 to decimal:
(1 x 2^7) + (1 x 2^6) + (1 x 2^5) + (0 x 2^4) + (1 x 2^3) + (0 x 2^2) + (0 x 2^1) + (0 x 2^0) = 128 + 64 + 32 + 8 = 232
Therefore, 11101000 in binary is equivalent to 232 in decimal.
Binary to Hexadecimal Conversion:
To convert a binary number to hexadecimal, the binary digits are grouped into sets of four. Each group is then converted to its equivalent hexadecimal digit. For example, when converting 10101010 to hexadecimal:
1010 1010 -> AA
Therefore, 10101010 in binary is equal to AA in hexadecimal.
By mastering these conversion techniques, you can unleash the power of binary and hexadecimal numbers in the digital realm. Embrace the challenge and elevate your numeracy skills to new heights!