Question

In the binary number system 100 + 1011 is equal to:

• A. 1000
• B. 1011
• C. 1110
• D. 1111

Answer 1

The correct option is D 1111

$(100{)}_2+(1011{)}_2=(0\times 2^0+0\times 2^1+1\times 2^2)+(1\times 2^0+1+2^1+0\times 2^2+1\times 2^3)$
= $(0+0+4)+(1+2+0+8)=(15{)}_{10}$
2 15
2 7 -1
2 3 -1
2 1 -1
0 -1
$\uparrow$ readup the remainders. or $(15{)}_{10}=(1111{)}_2$
ALTERNATIVELY :
0100 + 1011 = (1111)${}_2$
$(1111{)}_2=1\times 2^3+1\times 2^2+1\times 2^1+1\times 2^0=(15{)}_{10}$