**Title: Understanding Two’s Complement Representation in 8-bit Binary System**Assume numbers are represented in 8-bit two's complement representation. Show the calculation of the following:a. \(6 - 13\)b. \(-6 - 13\)---**Explanation:**In two's complement representation, positive numbers are represented as usual in binary, whereas negative numbers are represented by inverting the binary digits of the positive equivalent and adding one to the result. This representation allows for simple binary arithmetic and is commonly used in computer systems for signed number operations.To solve these computations, first convert the numbers to their 8-bit binary representations, perform the subtraction in binary by adding the two’s complement of the second number, and interpret the result.**Example Calculation:**1. **\(6 - 13\)**: - Convert \(6\) and \(13\) to binary. - Find the two’s complement of \(13\). - Add the binary of \(6\) to the two’s complement of \(13\).2. **\(-6 - 13\)**: - Convert \(-6\) and \(13\) to binary. - Find the two’s complement of both numbers. - Add the two’s complement of \(-6\) to the two’s complement of \(13\).These operations illustrate how subtractions are efficiently handled in binary using two’s complement, simplifying arithmetic operations within digital systems.

To perform subtraction using two's complement representation, you can follow these steps:Convert the…

Answered: Assume numbers are represented in 8-bit…

Engineering

Computer Science

Assume numbers are represented in 8-bit twos complement representation. Show the calculation of the following:

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: 6. Show how each of the following signed, decimal integers would be stored in 16-bit two's…

A: The number system uses a base and digit or symbol to represent a number. If the base of a number…

Q: How will the bit representation be expanded for unsigned number (unsigned short usx to unsigned ux)…

A: The datatypes in the domain of integer can be either signed or unsigned in nature. This nature is…

Q: Using eight bits representation, perform subtraction on the give numbers using the 2's complement of…

A: To find subtraction of 2 8-bit binary number, follow the below steps:-Step 1- find the 8-bit binary…

Q: 22. Determine the decimal value of 01110100 in 2's complement form

A: As per our guidelines only one question can be answered please post remaining question…

Q: 8. Perform the following additions. Assume that all numbers are in 8-bit 2’s complement notation.…

A: Given that, 10011001 +10111011 These two binary numbers are in the 8-bit 2's complement notation.

Q: a. -2.40625 b. 11.2265625 2) Given the following binary number: 1101.0111, what will be its…

A: Question 1: In IEEE 754 single-precision floating-point format, you are asked to provide the 32-bit…

Q: For 10 bits floating point representation using: seeeefffff, what is the bias for denormalized…

A: Please give positive ratings for my efforts. Thanks. ANSWER Qstn 1 : Number of bits for…

Q: 1)Using IEEE 754 representation for single precision floating point, give the 32- bit binary…

A: To represent floating-point numbers using IEEE 754 single-precision format, we need to consider the…

Q: We are using the simple model for floating point representation which is a 14-bit format, 5 bits for…

A: Given: We are using the simple model for floating point representation which is a 14-bit format, 5…

Q: Determine the base-six representation for each of the following numbers which are in base ten: A-…

Q: 6. Convert the following negative numbers into binary, using 2's complement form a) -23 using 8 bits…

A: Required: 6. Convert the following negative numbers into binary, using2's complement form

Q: a) Write IEEE floating point representation of the decimal number 3.14 (show work). (First, you need…

A: The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for…

Q: 6 Conyert decimal -2885 to hexadecimal.

A: 1. Divide the number by 16. 2. Use the quotient obtained for the next iteration. 3. Record the…

Question

**Title: Understanding Two’s Complement Representation in 8-bit Binary System**

Assume numbers are represented in 8-bit two's complement representation. Show the calculation of the following:

a. \(6 - 13\)

b. \(-6 - 13\)

---

**Explanation:**

In two's complement representation, positive numbers are represented as usual in binary, whereas negative numbers are represented by inverting the binary digits of the positive equivalent and adding one to the result. This representation allows for simple binary arithmetic and is commonly used in computer systems for signed number operations.

To solve these computations, first convert the numbers to their 8-bit binary representations, perform the subtraction in binary by adding the two’s complement of the second number, and interpret the result.

**Example Calculation:**

1. **\(6 - 13\)**:
- Convert \(6\) and \(13\) to binary.
- Find the two’s complement of \(13\).
- Add the binary of \(6\) to the two’s complement of \(13\).

2. **\(-6 - 13\)**:
- Convert \(-6\) and \(13\) to binary.
- Find the two’s complement of both numbers.
- Add the two’s complement of \(-6\) to the two’s complement of \(13\).

These operations illustrate how subtractions are efficiently handled in binary using two’s complement, simplifying arithmetic operations within digital systems.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: a) Subtracting 13 from 6:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

5. Show how each of the following signed, decimal integers would be stored in 8-bit two's complement code. Give your answer in hexadecimal. a. +100 C. -10 e. -127 L -32 g. b. -1 d. +88 f. -16 h. -128
1. Convert the following decimal numbers into their IEEE-754 single-precision (32-bit) representations. Give your answers in hexadecimal form. All intermediate steps must be clearly shown. A single result will not receive marks a. 655.34375 b. -1.875 c. 0.734375
5
Assume we have a 2's complement system with an 8-bit whole number part and a 2-bit fractional part. Find a decimal representation of 2's complements binary number 1110 0010.01 it expects a numeric entry. It will automatically suppress leading and trailing zeros. It will display your answer with commas every third digit.
degital design
In single precision (IEEE-754 standard), 8 bits are used for storing the exponent (the bias is 127), and 23 bits are used for storing the mantissa. (a) What are the smallest and the largest positive numbers that can be stored in single precision? (b) What is the smallest value of the mantissa that can be stored?
H - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values: (i)–1.0 (ii)– 0.0 (iii)256.015625
6. Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below. Show the sign, exponent, and mantissa (significand).b. 11.2265625
Find the binary representation for each of the following decimal represented numbers: 4, 8, 16, 32
1. unsigned binary and decimal representations.a. Give the 16-bit unsigned binary and hexadecimal representations of thedecimal number (2040).b. Give the 16-bit unsigned binary and decimal representations of the hexnumber (B2CF).
1. Write down the IEEE double-precision representation for the following decimal numbers: (a) 1.5, using round up. (b) 5.1, using round to nearest. (c) -5.1, using round towards 0. (d) -5.1, using round down.
To convert the decimal number 30 to an 8-bit binary number, use the following representation methods: a) the inverse of its complement: b) Excess-M:?