Conversion and Coding(12)10

Conversion and Coding(12)10

1100Conversion

Conversion and Coding(12)10

1100Conversion 00010010Coding(using BCD code for each digit)

BCD AdderDesign a circuit that calculates the Arithmetic addition of two decimal digits.

9 3 2

+

1carry

BCD Adder

Maximum sum is 9+9 + 1 = 19

Max digit Carry from previous digits

BCD adder (sum up to 9)Number C S8 S4 S2 S1

0 0 0 0 0 01 0 0 0 0 12 0 0 0 1 03 0 0 0 1 14 0 0 1 0 05 0 0 1 0 16 0 0 1 1 07 0 0 1 1 18 0 1 0 0 09 0 1 0 0 1

BCD adder (sum up to 9)Number C S8 S4 S2 S1

0 0 0 0 0 01 0 0 0 0 12 0 0 0 1 03 0 0 0 1 14 0 0 1 0 05 0 0 1 0 16 0 0 1 1 07 0 0 1 1 18 0 1 0 0 09 0 1 0 0 1

The sum is the same with BCD adder

BCD adder (sum is 10 to 19)

Number C S8 S4 S2 S110 1 0 0 0 011 1 0 0 0 112 1 0 0 1 013 1 0 0 1 114 1 0 1 0 015 1 0 1 0 116 1 0 1 1 017 1 0 1 1 118 1 1 0 0 019 1 1 0 0 1

BCD adder (sum is 10 to 19)

Number C S8 S4 S2 S1

10 1 0 0 0 011 1 0 0 0 112 1 0 0 1 013 1 0 0 1 114 1 0 1 0 015 1 0 1 0 116 1 0 1 1 017 1 0 1 1 118 1 1 0 0 019 1 1 0 0 1

K Z8 Z4 Z2 Z10 1 0 1 00 1 0 1 10 1 1 0 00 1 1 0 10 1 1 1 00 1 1 1 11 0 0 0 01 0 0 0 11 0 0 1 01 0 0 1 1

Binary sumBCD adder sum

BCD adder (sum is 10 to 19)

Number C S8 S4 S2 S1

10 1 0 0 0 011 1 0 0 0 112 1 0 0 1 013 1 0 0 1 114 1 0 1 0 015 1 0 1 0 116 1 0 1 1 017 1 0 1 1 118 1 1 0 0 019 1 1 0 0 1

K Z8 Z4 Z2 Z10 1 0 1 00 1 0 1 10 1 1 0 00 1 1 0 10 1 1 1 00 1 1 1 11 0 0 0 01 0 0 0 11 0 0 1 01 0 0 1 1

Binary sumBCD adder sum

BCD adder (sum is 10 to 19)

Number C S8 S4 S2 S1

10 1 0 0 0 011 1 0 0 0 112 1 0 0 1 013 1 0 0 1 114 1 0 1 0 015 1 0 1 0 116 1 0 1 1 017 1 0 1 1 118 1 1 0 0 019 1 1 0 0 1

K Z8 Z4 Z2 Z10 1 0 1 00 1 0 1 10 1 1 0 00 1 1 0 10 1 1 1 00 1 1 1 11 0 0 0 01 0 0 0 11 0 0 1 01 0 0 1 1

Binary sumBCD adder sum

+6

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

When is the result > 9Number K Z8 Z4 Z2 Z110 0 1 0 1 011 0 1 0 1 112 0 1 1 0 013 0 1 1 0 114 0 1 1 1 015 0 1 1 1 116 1 0 0 0 017 1 0 0 0 118 1 0 0 1 019 1 0 0 1 1

Binary sum

C = K +

When is the result > 9Number K Z8 Z4 Z2 Z110 0 1 0 1 011 0 1 0 1 112 0 1 1 0 013 0 1 1 0 114 0 1 1 1 015 0 1 1 1 116 1 0 0 0 017 1 0 0 0 118 1 0 0 1 019 1 0 0 1 1

Binary sum

C = K + Z8*Z4+

When is the result > 9Number K Z8 Z4 Z2 Z110 0 1 0 1 011 0 1 0 1 112 0 1 1 0 013 0 1 1 0 114 0 1 1 1 015 0 1 1 1 116 1 0 0 0 017 1 0 0 0 118 1 0 0 1 019 1 0 0 1 1

Binary sum

C = K + Z8*Z4+ Z8*Z2

BCD Adder

4-bit Adder

4-bit Adder

0 0 z8 z4 z2 z1

s8 s4 s2 s1

Cin

K