NIMCET 2026 — Computer PYQ
NIMCET | Computer | 2026what is the decimal equivalent of the 8-bit two's complement number 110100112?
Choose the correct answer:
- A.
−211
- B.
−45
(Correct Answer) - C.
−44
- D.
+211
−45
Explanation
To find the decimal equivalent of a negative number represented in two's complement, we can use the formula for an n-bit number bn−1bn−2...b0:
Value=−bn−1⋅2n−1+i=0∑n−2bi⋅2i
Given the 8-bit number 110100112:
The Most Significant Bit (MSB) is 1, which indicates the number is negative.
Calculation:
Value=−(1⋅27)+(1⋅26+0⋅25+1⋅24+0⋅23+0⋅22+1⋅21+1⋅20)
Value=−128+(64+0+16+0+0+2+1)
Value=−128+83
Value=−45
Explanation
To find the decimal equivalent of a negative number represented in two's complement, we can use the formula for an n-bit number bn−1bn−2...b0:
Value=−bn−1⋅2n−1+i=0∑n−2bi⋅2i
Given the 8-bit number 110100112:
The Most Significant Bit (MSB) is 1, which indicates the number is negative.
Calculation:
Value=−(1⋅27)+(1⋅26+0⋅25+1⋅24+0⋅23+0⋅22+1⋅21+1⋅20)
Value=−128+(64+0+16+0+0+2+1)
Value=−128+83
Value=−45