ASCII code and binary-to-Excess-3 converter

ASCII code

ASCII (American Standard Code for Information Interchange) is a 7-bit alphanumeric code that represents 128 characters: letters, digits, symbols and control characters. Example: 'A' = 65 = 100 0001, 'a' = 97 = 110 0001, '0' = 48 = 011 0000.

Binary (BCD) to Excess-3 code converter

Inputs: 4-bit binary/BCD digit $ABCD$ ($A$ = MSB), valid 0–9. Outputs: Excess-3 code $WXYZ$ = input + 3. Inputs 10–15 never occur, so they are don't cares (X).

K-map simplification

Minterms (don't cares $d = 10$–$15$):

• $W = \sum m(5,6,7,8,9) + d$
• $X = \sum m(1,2,3,4,9) + d$
• $Y = \sum m(0,3,4,7,8) + d$
• $Z = \sum m(0,2,4,6,8) + d$

K-map for $W$ (rows $AB$, columns $CD$):

          CD
 AB     00  01  11  10
 00   |  0 | 0 | 0 | 0 |
 01   |  0 | 1 | 1 | 1 |
 11   |  X | X | X | X |
 10   |  1 | 1 | X | X |

Groups: $A$ (rows 11 and 10), $BD$, $BC$.

Simplified expressions:

$$\begin{aligned} W &= A + BC + BD \\ X &= \bar B C + \bar B D + B\bar C\bar D \\ Y &= CD + \bar C\bar D \\ Z &= \bar D \end{aligned}$$

(Each equation can be checked against all ten rows of the truth table.)

Logic circuit (basic gates)

 A ----------------------------+
 B --+--[AND]-- BC ------------+--[OR]--- W
 C --+                         |
 B --+--[AND]-- BD ------------+
 D --+

 B'--+--[AND]-- B'C -----------+
 C --+                         |
 B'--+--[AND]-- B'D -----------+--[OR]--- X
 D --+                         |
 B --+                         |
 C'--+--[AND]-- BC'D' ---------+
 D'--+

 C --+--[AND]-- CD ------------+--[OR]--- Y
 D --+                         |
 C'--+--[AND]-- C'D' ----------+
 D'--+

 D ----[NOT]---------------------------- Z

NOT gates generate $\bar B$, $\bar C$ and $\bar D$; the $\bar D$ inverter also drives output Z directly. The circuit therefore uses 7 AND gates, 3 OR gates and 3 NOT gates.