Sign Extension in Various Number Representations | 2's Complement | Digital Logic скачать в хорошем качестве

Sign Extension in Various Number Representations | 2's Complement | Digital Logic

Sign Extension in Various Number Representations: Suppose we have an n-bit binary number written as: aₙ aₙ₋₁ ... a₁. Now, we want to store or copy this number in n + r bits (i.e., increase the number of bits by r). This is done differently depending on the number representation, but the value and sign of the number must remain the same. 1. Unsigned Representation: Add r zeros to the left of the number. Result: 000...0 aₙ aₙ₋₁ ... a₁ (with r zeros) Example: If r = 3, then the result is: 000 aₙ aₙ₋₁ ... a₁ 2. Sign-Magnitude Representation: Keep the most significant bit (MSB), which is aₙ, the same. Add r zeros after the MSB, then append the remaining bits (the magnitude part). Result: aₙ 000...0 aₙ₋₁ ... a₁ Example: If r = 3, then the result is: aₙ 000 aₙ₋₁ ... a₁ 3. 1's Complement Representation: Repeat the MSB (aₙ) r times to the left of the original number. Result: aₙ aₙ ... aₙ aₙ aₙ₋₁ ... a₁ (with r copies of aₙ) Example: If r = 3, then the result is: aₙ aₙ aₙ aₙ aₙ₋₁ ... a₁ 4. 2's Complement Representation: Same as 1's complement. Repeat the MSB (aₙ) r times to the left of the original number. Result: aₙ aₙ ... aₙ aₙ aₙ₋₁ ... a₁ Example: If r = 3, then the result is: aₙ aₙ aₙ aₙ aₙ₋₁ ... a₁ Related Video Lecture: ➤ Range of Binary Numbers in All Representations:    • Range of Signed Binary Numbers in Various ...   Crack GATE Computer Science Exam with the Best Course. ➤ Join "GO Classes #GateCSE Complete Course": https://www.goclasses.in/s/pages/gate... Join GO Classes #Gate2024 Complete Course here: https://www.goclasses.in/courses/GATE... ➤ Download GO Classes Android APP: https://play.google.com/store/apps/de... ---------------------------------------------------- #GoClasses Website : https://www.goclasses.in/ #GOClasses ALL Links : https://linktr.ee/goclasses ➤ Join GATEOverflow + GoClasses Combined TEST SERIES for Best Quality questions for GATE CSE Preparation, Here: https://gateoverflow.in/blog/14987/ga... ---------------------------------------------------- ➤Join GATE Overflow & GO Classes #Telegram Groups for GATE CSE Doubt Discussions: 1. https://t.me/GATECSE_Goclasses 2. https://t.me/gateoverflow_cse 3. https://t.me/goclasses_cse ---------------------------------------------------- ➤ Watch Complete Discrete Mathematics and Complete Engineering Mathematics Courses on GO Classes( FREE for ALL learners) : https://www.goclasses.in/s/store/ Complete #Discrete_Mathematics Course(FREE) Link : https://www.goclasses.in/courses/Disc... Complete #Engineering_Mathematics Course(FREE) Link : https://www.goclasses.in/courses/Engi... Know ALL about GO Classes GATE 2024 Course: https://www.youtube.com/live/47_lF9_N... Download GATEOverflow GATE Previous Years Questions(GATE CSE PYQs) Books here: https://github.com/GATEOverflow/GO-PD... ---------------------------------------------------- Feel free to Contact Us for any query. ➤ GO Classes Contact : (+91)63025 36274 (+91)9468930964 GO Classes Mail ID : contact@goclasses.in contact.goclasses@gmail.com #gatecse #gate2024 #goclasses #computerscience #computer_science