BCD SUM CORRECTION

Question

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

Comments

Is it A ?

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Yes. Could you please explain the logic?

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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 Z₈Z₄Z₂Z₁ 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. KZ₈'Z₄'Z₂Z_1.

We don't have any row in the Truth Table for numbers>19. So we put don't care in the cells where Z₈Z₄Z₂Z₁>0011. For eg.Z₈Z₄Z₂Z₁=0100 i.e.  K Z₈Z₄Z₂Z₁=1 0100 = (20)₁₀

 

Answer 1

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