Find the decimal representation of 0x8A1B assuming the hexadecimal number relates to the 2s complement representation form of a 16 bit binary number.

Question

BlackTom AI · Accepted Answer

We start by identifying what 0x8A1B represents in a 16-bit two's complement system.
The unsigned value of 0x8A1B is: 0x8A1B = 0x8A00 + 0x1B = 35328 + 27 = 35355.
Since the most significant bit is 1 (the 16th bit), this value is negative in 16-bit two's complement.
To find the signed value, compute 35355 - 65536 = -30181. This confirms the decimal representation.
Now evaluate each option:
- Option -30181: This matches the calculation above, so it is the correct two's complement decimal representation.
- Option -30180: This is off by 1 from the correct result, which could arise from misinterpreting the sign or miscomputing the wraparound; it does not match the actual two's complement value.
- Option 35358: This is close to the unsigned value 35355 but ignores the sign bit; it would be the positive interpretation if you treated the hex as unsigned rather than two's complement.
- Option 35359: Like 35358, this is another unsigned interpretation not consistent with a negative 16-bit two's complement number.
- Option None of these: Since we have found a matching value (-30181), this option is inaccurate.
In summary, the key insight is recognizing 0x8A1B as a negative 16-bit two's complement number and converting to decimal via 35355 − 65536 = -30181. The other options either ignore the sign bit or miscalculate the wraparound, leading to incorrect results.

CSE-12-02 Quiz 3 : Sequential Circuits, Signed Numbers, Decoders, Multiplexers

Find the decimal representation of 0x8A1B assuming the hexadecimal number relates to the 2s complement representation form of a 16 bit binary number.

查看解析

登录即可查看完整答案

类似问题

Suppose that 16-bit two's complement numbers are being employed. Consider the bit pattern: 1111 1111 1110 0100 What decimal integer most likely corresponds to these sixteen bits:

Suppose that 12-bit two's complement numbers are being employed. What decimal integer would give rise to the twelve-bit sequence 1111 1110 0010:

Suppose that 8-bit two's complement numbers are being employed. What bit pattern corresponds to the decimal integer value −50 (negative fifty):

Category: 16-bit Twos Complement 5 + 4 Assuming that all numbers are represented in 16-bit two's complement binary, what is the decimal value of the result of adding 5 and 4? Your answer must start with an initial sign, + or -. The rest of your answer must only contain decimal digits.

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 at position 14 Two values A = 11111111111111111111111010101 and B = 1111010101 are representations of 2's complement integers.A is largerA and B are equalYou can not tell from the information provided.B is larger

Question at position 8 What is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. AnswerWhat is the largest positive number one can represent in an 10-bit 2's complement code? Write your result in decimal. [input]

Category: Twos Complement -125 In eight bit two's complement notation what is the binary for -125

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单