Number Systems and Codes: Binary, Hexadecimal, Octal, and ASCII

Binary numbers are composed of only two digits, 0 and 1.

In hexadecimal, each digit represents a value from 0 to 15. 255 in decimal is 11111111 in binary, which is FF in hexadecimal.

To convert octal to decimal, multiply each digit by the corresponding power of 8 and add the results. 755 in octal is (7 * 8^2) + (5 * 8^1) + (5 * 8^0) = 448 + 40 + 5 = 503 in decimal.

ASCII codes are used to represent characters in computers. The ASCII code for 'A' is 65.

To convert hexadecimal to binary, convert each hexadecimal digit to its 4-bit binary equivalent. 1A in hexadecimal is 0001 1010 in binary, which is 11010.

Octal numbers consist of digits from 0 to 7. 101, 1111, and 1777 are not valid octal numbers because they contain digits greater than 7.

To convert decimal to hexadecimal, repeatedly divide the decimal number by 16 and write down the remainders. The remainders, read from bottom to top, give the hexadecimal representation. 1234 ÷ 16 = 77 with a remainder of 2. 77 ÷ 16 = 4 with a remainder of 13. 4 ÷ 16 = 0 with a remainder of 4. Therefore, 1234 in decimal is 4D2 in hexadecimal.

ASCII codes for digits start from 48 for '0' and go up to 57 for '9'.

To convert binary to decimal, multiply each digit by the corresponding power of 2 and add the results. 11001101 in binary is (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 128 + 64 + 8 + 4 + 1 = 205 in decimal.

Hexadecimal numbers consist of digits from 0 to 9 and letters A to F. G1H, 123Z, and ABCD are not valid hexadecimal numbers because they contain invalid characters.

To convert octal to binary, convert each octal digit to its 3-bit binary equivalent. 345 in octal is 011 100 101 in binary, which is 111001001.

ASCII codes for uppercase letters start from 65 for 'A' and go up to 90 for 'Z'.

To convert hexadecimal to decimal, multiply each digit by the corresponding power of 16 and add the results. 2AF in hexadecimal is (2 * 16^2) + (10 * 16^1) + (15 * 16^0) = 512 + 160 + 15 = 687 in decimal.

Binary numbers consist of only two digits, 0 and 1.

To convert decimal to binary, repeatedly divide the decimal number by 2 and write down the remainders. The remainders, read from bottom to top, give the binary representation. 1023 ÷ 2 = 511 with a remainder of 1. 511 ÷ 2 = 255 with a remainder of 1. 255 ÷ 2 = 127 with a remainder of 1. 127 ÷ 2 = 63 with a remainder of 1. 63 ÷ 2 = 31 with a remainder of 1. 31 ÷ 2 = 15 with a remainder of 1. 15 ÷ 2 = 7 with a remainder of 1. 7 ÷ 2 = 3 with a remainder of 1. 3 ÷ 2 = 1 with a remainder of 1. 1 ÷ 2 = 0 with a remainder of 1. Therefore, 1023 in decimal is 1111111111 in binary.