Question

What is the range of numbers that can be represented with n-bit signed magnitude binary? Can you give an example of the range for 8-bit binary?

a. The range for n-bit signed magnitude binary is from -2⁽ⁿ⁻¹⁾ to 2⁽ⁿ⁻¹⁾ - 1. For 8-bit binary, the range would be from -127 to 127.

b. The range for n-bit signed magnitude binary is from -2⁽ⁿ⁻¹⁾ to 2⁽ⁿ⁻¹⁾. For 8-bit binary, the range would be from -128 to 127.

c. The range for n-bit signed magnitude binary is from -2ⁿ to 2ⁿ - 1. For 8-bit binary, the range would be from -128 to 127.

d. The range for n-bit signed magnitude binary is from -2ⁿ to 2ⁿ. For 8-bit binary, the range would be from -127 to 127.

Answer 1

The range of numbers for n-bit signed magnitude binary is from −2^(n-1) to 2^(n-1) − 1. For an 8-bit example, this range is −128 to 127.

Step-by-step explanation:

The correct range of numbers that can be represented with n-bit signed magnitude binary is from −2(n-1) to 2(n-1) − 1. In signed magnitude binary representation, the first bit is used to represent the sign (0 for positive and 1 for negative), and thus, we have one less bit to represent the magnitude. This means the magnitude can range from 0 to 2(n-1) − 1. For negative numbers, we can represent from −2(n-1) to −1, and for positive numbers from 0 to 2(n-1) − 1.

Let's illustrate this with an 8-bit binary example: Here, n = 8, so the range is from −2(8-1) to 2(8-1) − 1, which simplifies to −128 to 127. This means that we can represent numbers from −128 to +127, inclusive, with an 8-bit signed magnitude binary number.

The correct answer to the student's question is therefore: b. The range for n-bit signed magnitude binary is from −2(n-1) to 2(n-1). For 8-bit binary, the range would be from −128 to 127.