Chapter 2, Problem 20E

a)

Explanation of Solution

Interpreting 10011110 as an unsigned number:

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

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

b)

Program Plan Intro

In signed magnitude representation, an extra bit is used to represent the sign of the number. This extra bit is called sign bit.

• The Most Significant Bit (MSB) in the binary number is referred as sign bit.
• In the signed magnitude representation, if the MSB is 0 it is treated as positive sign and if the MSB is 1 it is treated as negative sign.

c)

Program Plan Intro

One’s complement:

The binary numbers can be represented using one’s complement. Here, the value of every binary digit is complemented that is if the value is 1, it becomes 0 and if the value is 0 it becomes 1.

d)

Program Plan Intro

Two’s complement:

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

e)

Program Plan Intro

Excess-127 representation:

To get the excess-127 representation of a given number,

• Add the given number with the 127.
• Convert the obtained value to the binary representation.