11_{2} + 111_{2} + 1111_{2} + 11111_{2} = ? | vedclass

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Question

(B) To solve the addition of binary numbers,we perform column-wise addition following the rules of binary arithmetic $(0+0=0, 0+1=1, 1+1=10_{2})$:$11_

Vedclass · Accepted Answer

$111000_{2}$

Vedclass · Answer

(B) To solve the addition of binary numbers,we perform column-wise addition following the rules of binary arithmetic $(0+0=0, 0+1=1, 1+1=10_{2})$:$11_{2} = 3_{10}$$111_{2} = 7_{10}$$1111_{2} = 15_{10}$$11111_{2} = 31_{10}$Sum in decimal: $3 + 7 + 15 + 31 = 56_{10}$.Now,convert $56_{10}$ to binary:$56 \div 2 = 28$ remainder $0$$28 \div 2 = 14$ remainder $0$$14 \div 2 = 7$ remainder $0$$7 \div 2 = 3$ remainder $1$$3 \div 2 = 1$ remainder $1$$1 \div 2 = 0$ remainder $1$Reading remainders from bottom to top,we get $111000_{2}$.Alternatively,using column addition:$\begin{array}{r} 11 \ 111 \ 1111 \ + 11111 \ \hline 111000 \ \hline \end{array}$

$11_{2} + 111_{2} + 1111_{2} + 11111_{2} = ?$

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