Final answer:
The student's question involves arithmetic operations with both unsigned and signed binary numbers in different bit lengths. The operations include addition and subtraction, and the answers are within or exceed the range of the specified bit lengths, depending on the particular operation.
Step-by-step explanation:
The student has asked to perform several addition and subtraction operations with different types of numbers:
- 4-bit unsigned numbers addition: 14 + 7 equals 21. This operation uses simple arithmetic since both numbers are positive and within the range of 4-bit representation (0-15). However, the result 21 exceeds the 4-bit representation range.
- 4-bit unsigned numbers subtraction: 3 - 7 equals -4. Normally, you can't represent negative numbers with unsigned integers, but using the 'borrow' concept from subtraction, you technically get a result that cannot be represented in 4-bit unsigned format.
- 8-bit unsigned numbers addition: 248 + 32 equals 280. This operation is within the 8-bit range (0-255), so the result is a simple sum of the two numbers.
- 4-bit signed/2's complement numbers addition: 6 + 4 equals 10. The resulting number is within the representational range of 4-bit signed numbers (-8 to +7), so it can be accurately represented.
- 4-bit signed/2's complement numbers subtraction: -6 - 4 equals -10. When using 2's complement representation, -6 is represented as '1010' and 4 as '0100'. The operation will result in a number that exceeds the 4-bit signed range, but using 2's complement arithmetic, we get '0110' which would incorrectly represent +6 if we are limited to 4-bits.
When working with digital numbers and operations, it's vital to keep in mind the limitations posed by the number of bits you're working with, especially when it comes to representing both positive and negative numbers and the possibility of overflow.