Binary Number And Code Systems Quiz!

Explanation
The binary representation for 0xAC is 10101100.

Explanation
The hexadecimal representation of a binary number is obtained by grouping the binary digits into sets of four and converting each set into its corresponding hexadecimal digit. In this case, the binary number 100100101011 can be grouped as 1001 0010 1011. Converting each group into hexadecimal, we get 9 2 B. Therefore, the hexadecimal representation for the given binary number is 0x92B.

Explanation
The base 10 number 233 can be expressed as binary by repeatedly dividing it by 2 and noting the remainder. Starting with 233, the remainder is 1. Dividing 233 by 2 gives 116 with a remainder of 0. Dividing 116 by 2 gives 58 with a remainder of 0. Dividing 58 by 2 gives 29 with a remainder of 0. Dividing 29 by 2 gives 14 with a remainder of 1. Dividing 14 by 2 gives 7 with a remainder of 0. Dividing 7 by 2 gives 3 with a remainder of 1. Dividing 3 by 2 gives 1 with a remainder of 1. Finally, dividing 1 by 2 gives 0 with a remainder of 1. Reading the remainders from bottom to top gives the binary representation of 233 as 11101001.

Explanation
The base 10 number 312 can be converted to hexadecimal by dividing it by 16 repeatedly and noting down the remainders. Starting from the rightmost digit, the remainders are 12, 3, and 1. These remainders correspond to the hexadecimal digits C, 3, and 1 respectively. Therefore, the hexadecimal representation of 312 is 0x138.

Explanation
The binary equivalent for decimal number 9 is 1001. In binary, each digit represents a power of 2, starting from the rightmost digit being 2^0, then 2^1, 2^2, and so on. To convert decimal 9 to binary, we divide it by 2 repeatedly and record the remainders. The remainders, read from bottom to top, give us the binary representation. In this case, when we divide 9 by 2, we get a quotient of 4 and a remainder of 1. Dividing 4 by 2 gives us a quotient of 2 and a remainder of 0. Finally, dividing 2 by 2 gives us a quotient of 1 and a remainder of 0. Reading the remainders from bottom to top, we get 1001.

Explanation
The binary equivalent for the hexadecimal number 2A6 is 001010100110.

Explanation
The decimal equivalent for the hexadecimal number 3B is 59. In hexadecimal, each digit represents a value from 0 to 15. The digit 3 represents 3 in decimal, and the digit B represents 11 in decimal. To convert hexadecimal to decimal, we multiply each digit by the corresponding power of 16 and add them together. In this case, 3 multiplied by 16^1 (16) plus B multiplied by 16^0 (11) equals 48 + 11, which equals 59 in decimal.

Explanation
The given codeword is 011 1000. To attach an EVEN parity, we need to count the number of 1s in the codeword. If the count is even, we append a 0 to the codeword. If the count is odd, we append a 1. In this case, there are 3 1s in the codeword, which is an odd count. Therefore, we append a 1 to the codeword to achieve an EVEN parity.

Explanation
The binary number 11001 can be converted to decimal by multiplying each digit by the corresponding power of 2 and adding them together. In this case, the calculation would be: (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 16 + 8 + 0 + 0 + 1 = 25. Therefore, the decimal equivalent for the binary number 11001 is 25.