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Conversion and Coding (12)10

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Conversion and Coding (12)10 1100 Conversion

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**Conversion and Coding (12)10 00010010 1100 Coding Conversion**

(using BCD code for each digit) Conversion

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**BCD Adder Design a circuit that calculates the**

Arithmetic addition of two decimal digits. 9 + 3 1 2 carry

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**BCD Adder Maximum sum is 9+9 + 1 = 19 Max digit**

Carry from previous digits

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BCD adder (sum up to 9) Number C S8 S4 S2 S1 1 2 3 4 5 6 7 8 9

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**BCD adder (sum up to 9) Number C S8 S4 S2 S1 1 2 3 4 5 6 7 8 9**

1 2 3 4 5 6 7 8 9 The sum is the same with BCD adder

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**BCD adder (sum is 10 to 19) Number C S8 S4 S2 S1 10 1 11 12 13 14 15**

11 12 13 14 15 16 17 18 19

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**BCD adder (sum is 10 to 19) C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18**

Binary sum Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1

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**BCD adder (sum is 10 to 19) C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18**

Binary sum Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1

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**BCD adder (sum is 10 to 19) +6 C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17**

Binary sum Number C S8 S4 S2 S1 10 1 11 12 13 14 15 16 17 18 19 K Z8 Z4 Z2 Z1 1 +6

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**Algorithm for BCD Adder**

If sum is up to 9 Use the regular Adder. If the sum > 9 Use the regular adder and add 6 to the result

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**When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18**

Binary sum Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19 C = K +

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**When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18**

Binary sum Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19 C = K + Z8*Z4+

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**When is the result > 9 K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18**

Binary sum Number K Z8 Z4 Z2 Z1 10 1 11 12 13 14 15 16 17 18 19 C = K + Z8*Z4+ Z8*Z2

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BCD Adder 4-bit Adder Cin z8 z4 z2 z1 4-bit Adder K s8 s4 s2 s1

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