Understanding 8-bit Signed Binary Values and Carry & Overflow Flags
Representing Decimal Numbers as 8-bit Signed Binary Values
To represent decimal numbers as 8-bit signed binary values in the 2's complement number system, you need to follow a few steps. First, determine the sign of the number (positive or negative). For positive numbers, convert the absolute value to binary. For negative numbers, convert the absolute value to binary and then take the 2's complement by inverting the binary digits and adding 1. For example, to represent +210 as an 8-bit signed binary value, convert 210 to binary (11010010), preserving the sign bit (0 for positive). To represent -121 in the 2's complement form, convert 121 to binary (1111001), invert the bits (0000110), and add 1 to get the final value as 0000111.
Carry and Overflow Flags
The carry and overflow flags in a 4-bit system can be determined by examining the result of the addition operation. The carry flag is set when a carry-out occurs from the most significant bit. The overflow flag is set when the signs of the operands are the same but the sign of the result is different. For example, in the operation 0100 + 0010, the carry flag would not be set (as there is no carry-out from the most significant bit), and the overflow flag would also not be set since the signs of the operands are the same and the sign of the result is also the same. Similarly, you can determine the flags for the other operations.
Questions:
1. How do you represent decimal numbers as 8-bit signed binary values in the 2's complement number system?
2. What are the carry and overflow flags in a 4-bit system, and how are they determined?
Answers:
1. To represent decimal numbers as 8-bit signed binary values in the 2's complement number system, convert the absolute value to binary and determine the sign. The carry and overflow flags can be determined by examining the results of the addition operations.
2. To determine the carry and overflow flags in a 4-bit system, examine the result of the addition operation. The carry flag is set when there is a carry-out from the most significant bit, while the overflow flag is set when the signs of the operands are the same but the sign of the result is different.