1.1 Number System Conversion

To convert decimal to binary, divide the decimal number by 2 and record the remainders. For example, converting 150 to binary: 150÷2 = 75 remainder 0, 75÷2 = 37 remainder 1, 37÷2 = 18 remainder 1, 18÷2 = 9 remainder 0, 9÷2 = 4 remainder 1, 4÷2 = 2 remainder 0, 2÷2 = 1 remainder 0, 1÷2 = 0 remainder 1. The binary result is 10010110. To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right) and sum the results. For example, for 10010100: 1×2^7 + 0×2^6 + 0×2^5 + 1×2^4 + 0×2^3 + 1×2^2 + 0×2^1 + 0×2^0 = 128 + 16 + 4 = 148.

To convert decimal to hexadecimal, divide the decimal number by 16 and record the remainders. For example, 55÷16 = 3 remainder 7, so the hexadecimal is 37. To convert hexadecimal to decimal, multiply each hexadecimal digit by 16 raised to the power of its position (starting from 0 on the right) and sum the results. For example, for 1AB: 1×16^2 + 10×16^1 + 11×16^0 = 256 + 160 + 11 = 427.

To convert binary to hexadecimal, group the binary digits into groups of 4 from the right and convert each group to a hexadecimal digit. For example, 101111001001 becomes 1011 (B), 1100 (C), 1001 (9), so the hexadecimal is BC9. To convert hexadecimal to binary, convert each hexadecimal digit to a 4 - bit binary number. For example, for BC9: B is 1011, C is 1100, 9 is 1001, so the binary is 101111001001.