By M. Morris R. Mano, Charles R. Kime

*For classes in good judgment and desktop design.*

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** Logic and laptop layout Fundamentals ** is a completely up to date textual content that makes common sense layout, electronic process layout, and computing device layout on hand to readers of all degrees. The

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**Extra info for Logic and computer design fundamentals**

**Example text**

The conversion of a decimal number to binary can be easily achieved by a method that successively subtracts powers of two from the decimal number. To TABLE 1-2 Powers of Two n 2n n 0 1 2 3 4 5 6 7 1 2 4 8 16 32 64 128 8 9 10 11 12 13 14 15 2n 256 512 1,024 2,048 4,096 8,192 16,384 32,768 n 2n 16 17 18 19 20 21 22 23 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608 18 CHAPTER 1 / DigiTAl SySTEmS AnD infoRmATion convert the decimal number N to binary, irst ind the greatest number that is a power of two (see Table 1-2) and that, subtracted from N , produces a positive difference.

Each gate performs a speciic logical operation. The outputs of gates are applied to the inputs of other gates to form a digital circuit. In order to describe the operational properties of digital circuits, we need to introduce a mathematical notation that speciies the operation of each gate and that can be used to analyze and design circuits. This binary logic system is one of a class of mathematical systems generally called Boolean algebras (after the English mathematician George Boole, who in 1854 published a book introducing the mathematical theory of logic).

The letters of the alphabet are used to supplement the digits when r is 10 or more. The hexadecimal number system is a base 16 system with the irst 10 digits borrowed from the 1-3 / number Systems 19 TABLE 1-3 Numbers with Different Bases Decimal Binary (base 10) (base 2) Octal (base 8) Hexadecimal (base 16) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 00 01 02 03 04 05 06 07 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 A B C D E F 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 decimal system and the letters A, B, C, D, E, and F used for the values 10, 11, 12, 13, 14, and 15, respectively.