Question
25. Assume a 24-bit word on a computer. In these 24 bits, we wish to represent the value 295.
a) If our computer uses even parity, how would the computer represent the decimal value 295?
b) If our computer uses 8-bit ASCII and even parity, how would the computer represent the string 295?
c) If our computer uses packed BCD, how would the computer represent the number +295?
Answer
a)
If our computer uses even parity and we want to represent the decimal value 295 in a 24-bit word, we first convert 295 to binary:
295 (decimal) = 100100111 (binary)
To include even parity, we need to add one additional parity bit to the 24-bit word to ensure an even number of 1s. The resulting representation would be:
Parity bit + Data bits: 1 00100111
b)
If our computer uses 8-bit ASCII and even parity, each character in the string "295" would be represented using 8 bits in ASCII encoding. Here is how each character would be represented:
"2" in ASCII: 00110010 "9" in ASCII: 00111001 "5" in ASCII: 00110101
Including even parity for each character, the representation of the string "295" would be:
Parity bit + ASCII bits: 1 00110010 0 00111001 0 00110101
c)
If our computer uses packed BCD (Binary Coded Decimal), each digit in the number +295 would be represented using 4 bits. The packed BCD representation of +295 would be:
+2: 0010 +9: 1001 +5: 0101
Therefore, the packed BCD representation of +295 would be: 0010 1001 0101