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Q) Let the binary sum after BCD addition is stored in K, Z8, Z4, Z2, and Z1. Then the condition for a correction and output carry can be expressed as C =

A) K + Z8 Z4 + Z8 Z2 B) K + Z8 Z4 + Z4 Z2 C) K + Z8 Z2 + Z8 Z1 D) K + Z4 Z2 + Z2 Z1

A) K + Z8 Z4 + Z8 Z2 B) K + Z8 Z4 + Z4 Z2 C) K + Z8 Z2 + Z8 Z1 D) K + Z4 Z2 + Z2 Z1

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Since it will be very time consuming to draw a K-map of 5 variables, you can do it in this way i.e. by dividing Z_{8}Z_{4}Z_{2}Z_{1 }in two groups -> one in which K=0 and other in which K=1.

So for instance, the cell 3 in 2nd K-map corresponds to 1 0011 i.e. KZ_{8}'Z_{4}'Z_{2}Z_{1.}

We don't have any row in the Truth Table for numbers>19. So we put don't care in the cells where Z_{8}Z_{4}Z_{2}Z_{1}>0011. For eg.Z_{8}Z_{4}Z_{2}Z_{1}=0100 i.e. **K** Z_{8}Z_{4}Z_{2}Z_{1}=**1** 0100 = (20)_{10}

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we add bcd correction if there is

a final carry 1001 + 1001 --------------------- 1 0010 here K=1 hence we add 0110 for correction |
the result of sum of individual bcd digit is greater than 9 0110 + 0011 ------------------------ 1010 here the result is 1010 which is 10 in binary but not in bcd. to correct it add 0110 |

hence for correction to be added either K = 1 or result out of range

for the following cases we'll get out of range

$z_8$$z_4$$z_2$$z_1$

1010

1011

11xx

which is $z_8$$z_2$ + $z_8$$z_4$

option A) K + $z_8$$z_2$ + $z_8$$z_4$ is correct

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