NIMCET Previous Year Questions (PYQs) – 1s Complement 2s Complement – Page 1 of 2

✅ Given Information:

An 8-bit number in 2's complement form can represent values from $-2^{n-1}$ to $2^{n-1}-1$.

✅ Step 1: Calculate the smallest integer:

Smallest value = $-2^{8-1}=-2^7=-128$

✅ Final Answer:

The smallest integer that can be represented by an 8-bit number in 2's complement form is: -128

 Maximum & Minimum in 16-bit 2's Complement

 Total Bits: 16

Format: 1 sign bit + 15 magnitude bits

• Maximum (positive): 0111 1111 1111 1111(2) = +32,767
• Minimum (negative): 1000 0000 0000 0000(2) = −32,768

✅ Final Answer:
Minimum = −32,768
Maximum = +32,767

2's Complement Addition (4-bit)

Given: 1101 and 0100 (in 2’s complement)

Step-by-step:

• 1101 = −3 (in decimal)
• 0100 = +4 (in decimal)
• Sum = −3 + 4 = +1
• +1 in 4-bit 2’s complement = 0001

✅ Final Answer: 0001

2's Complement Addition (8-bit)

Given:

• A = 11111111 → (−1)
• B = 11111111 → (−1)

Sum: −1 + (−1) = −2

Convert −2 to 8-bit 2's complement:

• +2 = 00000010
• Invert = 11111101
• Add 1 = 11111110

✅ Final Answer: 11111110

Binary to Decimal: 2's Complement Conversion

Given binary numbers:

• 11001 (5-bit)
• 1001 (4-bit)
• 111001 (6-bit)

Step-by-step (2's complement):

• Each starts with 1 → negative number
• Convert by inverting and adding 1
• All result in binary 0111 → decimal 7
• So final value = −7

✅ Final Answer: Each binary number corresponds to the decimal number −7.