Chapter 3, Problem 4PE

Program Plan Intro

Base-2:

Base-2 number system consists of binary numbers “0” and “1”. The base-2 number system is a positional notation with a radix of 2.

Base-10 number system:

Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.

Program Plan Intro

Base 10:

Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.

Base-8:

Base-0 number system uses the value 0 through 7. The base-8 number system is a positional notation with a radix of 8.

Program Plan Intro

Base 10:

Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.

Base-16:

The base 16 represents the hexadecimal number system. Hexadecimal number system consists of sixteen digits from 0 to 9, and from 10 to 15 is represented in the form of letters from A to F.

Explanation of Solution

Representing ${(515)}_{10}$ in 16-bit excess notation:

To represent a positive decimal number in 16-bit excess notation, the binary equivalent of the number is added to $1000000000000000$.

Binary equivalent of number 515 represented 16 bits: $0000001000000011$

  $\begin{array}{l}1000000000000000\\ +0000001000000011\\ --------------\\ 1000001000000011\end{array}$

Therefore, ${(515)}_{10}$

Explanation of Solution

Representing ${(515)}_{10}$ in 16-bit two’s complement:

The two’s complement notation of any non-negative decimal number is the decimal equivalent of number. So, the binary equivalent of ${(515)}_{10}$ in 16 bit format is $0000001000000011$.

Therefore, the two’s complement notation of ${(515)}_{10}$ is $0000001000000011$.

Representing ${(-515)}_{10}$ in 16-bit two’s complement:

The two’s complement notation of negative decimal number is calculated by adding 1 to the complement of the binary equivalent of the number