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Why do we use two's complement to represent negative numbers in binary? Choose all that apply. Group of answer choices So that there is only one representation of 0 So that we can perform addition without worrying about the sign of the numbers So that we can use the most significant bit as a sign bit

Question

Why do we use two's complement to represent negative numbers in binary?

Choose all that apply.

Group of answer choices

So that there is only one representation of 0

So that we can perform addition without worrying about the sign of the numbers

So that we can use the most significant bit as a sign bit

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Solution

All of the given choices are correct reasons for using two's complement to represent negative numbers in binary. Here's why:

  1. "So that there is only one representation of 0": In two's complement, zero is uniquely represented as a string of all zeros. This is not the case in one's complement, where zero has two representations: a string of all zeros and a string of all ones.

  2. "So that we can perform addition without worrying about the sign of the numbers": Two's complement allows us to add numbers together regardless of their sign. The binary arithmetic works out such that if you add a positive number and a negative number together (represented in two's complement), you get the correct answer.

  3. "So that we can use the most significant bit as a sign bit": In two's complement, the most significant bit is used as a sign bit. If the most significant bit is 1, the number is negative. If it is 0, the number is positive. This makes it easy to determine the sign of a number at a glance.

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Similar Questions

In binary system each and every number and its sign are represented by using only thesetwo digits 0 and 1. As the negative and positive signs cannot be written directly in binarysystem. The alternative method to represent negative and positive numbers is the 2’scomplement method. It has an interesting property that the binary arithmetic operationcan be performed easily on signed or unsigned numbers. Compute the following binaryarithmetic operations using 2’s complement method. Show all the steps clearly. (LO 01)(2*5 = 10 Marks)a) Sum of -30 and 17b) Sum of -42 and -15c) Sum of -13 and -16d) Multiplication of -8 by 6e) Multiplication of -11 by -9

In the case of  4-bit binary numbers (length 4 bit), how do we represent “-4” in 2’s complement format?

Suppose that 8-bit two's complement numbers are being employed. What bit pattern corresponds to the decimal integer value −50 (negative fifty):Group of answer choices0011001001001110110011101100110111001111

The range of positive numbers possible in an 8-bit two's complement system is:

erform six bit signed two’s complement arithmetic operation on (−15)10 +(+65)10

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