Question 10.16: Convert the following decimal numbers to BCD and add them. C......
Convert the following decimal numbers to BCD and add them. Convert the result back to decimal to check your answer.
(a) 52 + 63 (b) 78 + 69
Step-by-Step
\begin{array}{l} \text{(a)}& 52 &=& 0101 & 0010 \\ &+63 &=& \underline{0110 }& \underline{0011} \\ &\text{Sum }&=& 1011 & 0101 \\ &&&&\nwarrow \\ &\text{Add }6 &= & \underline{0110 }& &&\text{invalid BCD number} \\&&& 1~ 0001 &0101 &=& 0001 \quad 0001 \quad0101_{BCD} \\ &&&&&=& \quad\overset{\nwarrow }{1}\qquad \overset{\uparrow }{1} \qquad \overset{\nearrow }{5_{10}} \end{array} .
\begin{array}{l} \text{(b)} & 78 &=& 0111 & 1000 & \\ &+69 &=& \underline{0110 }& \underline{1001} &\swarrow \text{ Both groups of 4 BCD bits are invalid}\\ &\text{Sum }&=& 1110 & 0001 \\ &&&& \nwarrow \\ &&&&\text{carry} \\ &\text{Add }6& =& \underline{~~~~~~~~} & \underline{0110} \\ &&&1110 & 0111 \\ &\text{Add }6 &=& \underline{0110} & \underline{~~~~~~~~} \\ &&&10100& 0111 &= 0001 \quad 0100 \quad 0111_{BCD} \\ &&&&&= \quad\overset{\nwarrow }{1} \qquad \overset{\uparrow }{4} \qquad\overset{\nearrow }{7_{10}}\end{array}Related Answered Questions
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