Category: 4-bit Twos Complement -5 + -5

Assuming that all numbers are represented in 4-bit two's complement binary, what is the decimal value of the result of adding -5 and -5? Your answer must start with an initial sign, + or -. The rest of your answer must only contain decimal digits.

Question

Category: 4-bit Twos Complement -5 + -5

Assuming that all numbers are represented in 4-bit two's complement binary, what is the decimal value of the result of adding -5 and -5? Your answer must start with an initial sign, + or -. The rest of your answer must only contain decimal digits.

BlackTom AI · Accepted Answer

We start by restating the problem in plain terms: adding -5 and -5 using 4-bit two's complement representation.

First, recall the 4-bit two's complement range is from -8 to +7. Values outside this range cannot be represented without overflow.

Represent -5 in 4-bit two's complement: take +5 as 0101, invert to 1010, add 1 to get 1011. So -5 is represented as 1011.

Add the two 4-bit representations: 1011 + 1011.
- Adding bit by bit: 1+1 = 0 with carry 1; next 1+1+carry1 = 1 with carry 1; next 0+0+carry1 = 1 with carry 0; last 1+1+carry0 = 0 with carry 1. The full sum is 1 0110, where the leftmost 1 is the carry out of the 4th bit.

In 4-bit arithmetic we discard the carry out and keep the lowest 4 bits: 0110.

The 4-bit value 0110 corresponds to +6 in decimal, which shows that overflow occurred (the true mathematical result is -10, which cannot be represented in 4 bits).

Because the problem statement requires the answer to start with a sign (+ or -) and then only decimal digits, the only representable 4-bit outcome is +6, which would be written as +6. The given proposed answer of -2 does not match the 4-bit wraparound result (+6) and does not reflect the actual decimal value that the 4-bit system would display after overflow.

In short, the operation leads to overflow in 4-bit two's complement, producing a wrapped result of +6, while the mathematically correct sum is -10 and cannot be represented in 4 bits; since -2 does not align with either interpretation, it is incorrect for this scenario.

4520_COMP_SCI_X_0005 Week 8 Exam

Category: 4-bit Twos Complement -5 + -5 Assuming that all numbers are represented in 4-bit two's complement binary, what is the decimal value of the result of adding -5 and -5? Your answer must start with an initial sign, + or -. The rest of your answer must only contain decimal digits.

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