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iPad 2:57 PM * 70% 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 2 BDC Encoding Digit | A3 | A2 | A1 Ao 0 0 0 0 0 0 If one needs to sum two BDC digits, two 4-bit binary adders can be combined, as shown in Figure 2. B3 A B2 Az B A1 B Ap 4-bit adder 4-bit adder Figure 2 BDC Digit Adder where Aa-o and B3o are two BDC digits, S3-o and Cout are their BDC digit sum and BDC carry out, and Zso and Kaut are intermediary binary sum and carry out. Page 3 of 5 iPad 2:57 PM * 70%- Table 3 outlines the relationship between KaurZs a and CoutS3 o. Note that KoutZs a can only take values ranging between 00000) and 10010p), i.e. and 18zo Table 3 BDC Encodin 0 000 1 0 00 0 1 0 00 1 0 000 1 0 0 00 1 1 0 00 1 1 0 01 0 0 0010 0 0 010 1 0 010 1 0 01 1 0 0 01 0 0 01 1 1 0 01 1 0 1 00 0 010 00 0 1 0 1 0 10 0 00 0 1 0 1 1 0 0 0 1 0 1 10 0 10 0 10 0 1 1010 0 1 1 0 1 1 1 0 01 00 1 0 0 0 0 1 011 0 1 0 00 1 1 011 1 1 0 0 10 1 1 0 0 0 Page 4 of 5 iPad 2:57 PM * 70% 1) From Table 3, show that Cout Kout + ZZz tZZi. You can also use a K-Map to do so. 00 01 11 10 KoutZ3 01 10 2) From Table 3, show that So Zsa+OCourCourOpy N.B. The symbol"+" means a binary addition, not the logical operator OR. Page 5 of 5 iPad 2:57 PM * 70% 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 2 BDC Encoding Digit | A3 | A2 | A1 Ao 0 0 0 0 0 0 If one needs to sum two BDC digits, two 4-bit binary adders can be combined, as shown in Figure 2. B3 A B2 Az B A1 B Ap 4-bit adder 4-bit adder Figure 2 BDC Digit Adder where Aa-o and B3o are two BDC digits, S3-o and Cout are their BDC digit sum and BDC carry out, and Zso and Kaut are intermediary binary sum and carry out. Page 3 of 5 iPad 2:57 PM * 70%- Table 3 outlines the relationship between KaurZs a and CoutS3 o. Note that KoutZs a can only take values ranging between 00000) and 10010p), i.e. and 18zo Table 3 BDC Encodin 0 000 1 0 00 0 1 0 00 1 0 000 1 0 0 00 1 1 0 00 1 1 0 01 0 0 0010 0 0 010 1 0 010 1 0 01 1 0 0 01 0 0 01 1 1 0 01 1 0 1 00 0 010 00 0 1 0 1 0 10 0 00 0 1 0 1 1 0 0 0 1 0 1 10 0 10 0 10 0 1 1010 0 1 1 0 1 1 1 0 01 00 1 0 0 0 0 1 011 0 1 0 00 1 1 011 1 1 0 0 10 1 1 0 0 0 Page 4 of 5 iPad 2:57 PM * 70% 1) From Table 3, show that Cout Kout + ZZz tZZi. You can also use a K-Map to do so. 00 01 11 10 KoutZ3 01 10 2) From Table 3, show that So Zsa+OCourCourOpy N.B. The symbol"+" means a binary addition, not the logical operator OR. Page 5 of 5
