Question

EXERCISE 3 Binary-coded decimal (BCD) is a binary encoding of decimal numbers where each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table Table 1 BDC Encoding 0 0 0 0 If one needs to sum two BDC digits, two 4-bit binary adders can be combined, as shown in Figure 1 4-bit adder 0 out 4-bit adder Figure 1 BDC Digit Adder

Answer 1

The Resultant count should be 1 when the addition of two BCD numbers results a carry or the sum of two BCD numbers exceed the decimal value '9' so count = k_at + F(z_3, z_2, z_1, z_0) whre F(z_3, z_2, z_1, z_0) is an SOP expression that results is 1 when BCD number 1X invalid The corresponding K map is So, F(z_3, z_2, z_1, z_0) = z_2 z_2 + z_2 z_1 count = k_out + z_3 z_2 + z_2 z_1 c_out = k_out + z_3 z_2 + z_3 z_1 \r\n From table (3) when z_3 -0 is 0000 through 1001 and c_out = 0 we can see that z_3 - 0 = s_3 - 0 = s_3 - 0 + 0000 s_3 -0 = z_3 -0 + 0 c_out c_out 0 s_3 - 0 + 0 c_out c_out when c_out = 1 z_3 = 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 \r\n