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That includes a powerful emphasis at the basics underlying modern common sense layout utilizing description languages, synthesis, and verification, this ebook makes a speciality of the ever-evolving functions of easy machine layout strategies with powerful connections to real-world expertise. remedy of good judgment layout, electronic procedure layout, and machine layout. excellent for self-study via engineers and computing device scientists.
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In other words, if X = 1, then Z = O; but if X = 0, then Z = 1. The NOT opera tion is also referred to as the complement operation, since it changes a 1 to0 and a0 to1. Binary logic resembles binary arithmetic, and the operations AND and OR have similarities to multiplication and addition, respectively. This is why the sym bols used for AND and OR are the same as those used for multiplication and addi tion. However, binary logic should not be confused with binary arithmetic. One should realize that an arithmetic variable designates a number that may consist of D 2-1 I Binary Logic and Gates 37 many digits, whereas a logic variable is always either a 1 or a 0.
In (b) , we evaluate X and Y and then AND them together. The result is the same D TABLE2-4 Truth Tables to Verify DeMorgan's Theorem (a) x y x+v 0 0 0 0 1 1 1 0 1 1 1 1 x y 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 X+Y (b) x y X·Y 44 0 CHAPTER 2 I COMBINATIONAL LOGIC CIRCUITS for the four binary combinations of X and Y, which verifies the identity of the equation. Note the order in which the operations are performed when evaluating an expression. In part (b) of the table, the complement over a single variable is evalu ated first, followed by the AND operation, just as in ordinary algebra with multipli cation and addition.
Here is one such algorithm: 1. Draw lines to bound the expected BCD decades to the left of the binary number. 2. Move the binary number one bit to the left. Add 0011 to each BCD decade containing a binary value> 0100. 4. Repeat steps 2 and 3 until the last bit in the binary number has been moved into the least significant BCD decade position. 5. Read the BCD result. (a) Execute the algorithm (b) Execute the algorithm for the binary number 1111000. for the binary number 01110010111. 1-22. What bit position in an ASCII code must be complemented to change the ASCII letter represented from uppercase to lowercase and vice versa?