The state of a 12-bit register is 100010010111. What is its content if it represents (a) Three decimal digits in BCD? (b) Three decimal digits in the excess-3 code? (c) Three decimal digits in the 84-2-1 code? (d) A binary number?

(a) Three decimal digits in BCD: BCD stands for Binary Coded Decimal. It is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four. In this case, we have a 12-bit register, so we can divide it into three 4-bit groups, each representing a decimal digit in BCD.

1000 1001 0111

So, the three decimal digits are 8, 9, and 7.

(b) Three decimal digits in the excess-3 code: Excess-3 is a non-weighted code used to express decimal numbers. The code derives its name from the fact that each digit is represented by the binary equivalent of the digit value plus three.

1000 (8-3) = 5 1001 (9-3) = 6 0111 (7-3) = 4

So, the three decimal digits are 5, 6, and 4.

(c) Three decimal digits in the 8-4-2-1 code: The 8-4-2-1 code is another name for BCD, so the answer is the same as in part (a): 8, 9, and 7.

(d) A binary number: If the 12-bit register represents a binary number, then we simply convert the binary number to decimal.

100010010111 (binary) = 2255 (decimal)