Chapter 2, Problem 23E

a)

Explanation of Solution

Determining the decimal equivalent for unsigned number 11111100:

Step 1: Multiply the given binary number with the positive integers for base 2.

$2^7\times 1+2^6\times 1+2^5\times 1+2^4\times 1+2^3\times 1+2^2\times 1+2^1\times 0+2^0\times 0$

Step 2: Add all the values to get the final result.

$128+64+32+16+8+4=252$

Therefore, the decimal equivalent of the number represented in unsigned number 11111100 is $252$.

Determining the decimal equivalent for unsigned number 01110000:

Step 1: Multiply the given binary number with the positive integers for base 2

b)

Program Plan Intro

Two’s complement:

Two’s complement is another way of representing the binary numbers. To implement the two’s complement to the number, the given binary number should be one’s complemented and then add 1 to the result obtained after one’s complement.

c)

Explanation of Solution

Interpreting 11111100 as a signed magnitude representation:

In the given binary number, the MSB bit is 1. Hence, the binary number is negative.

Step 1: Multiply the given binary number with the positive integers for base 2.

$2^6\times 1+2^5\times 1+2^4\times 1+2^3\times 1+2^2\times 1+2^1\times 0+2^0\times 0$

Step 2: Add all the values to get the final result.

$64+32+16+8+4=124$

Therefore, the decimal equivalent of the number represented in signed magnitude is $-124$

Interpreting 01110000 as a signed magnitude representation:

Step 1: Multiply the given binary number with the positive integers for base 2