1. CSCE 211: Digital Logic Design
Chin-Tser Huang
University of South Carolina

2. Chapter 1: Introduction

3. Digital Systems They are everywhere!
They are usually binary: operating on two-valued signals
Take an arbitrary number of inputs and produce an arbitrary number of outputs
Some systems require a timing signal called clock
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5. Examples
A system with three inputs, A, B, and C, and one output Z, such that Z = 1 if and only if two of the inputs are 1
A system with eight inputs, representing two 4-bit binary numbers, and one 5-bit output, representing the sum
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6. Examples
A system with one input, A, plus a clock, and one output, Z, which is 1 iff the input was one at the last three consecutive clock times
A traffic controller on two streets: the light is green on each street for a fixed period of time, then goes to yellow for another fixed period and finally to red. The only input to this system is the clock
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7. Truth Table Describe the behavior of a digital system in tabular form
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9. A Brief Review of Number Systems
Integers are usually written using a positional number system
N = an-1rn-1 + an-2rn-2 + … + a2r2 + a1r + a0
where 0  ai < r
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10. Conversion between Number Systems
How to convert from binary to decimal? Evaluate the power series
Example: = ?
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11. Conversion between Number Systems
How to convert from decimal to binary? Two algorithms
Repeatedly subtract from the number the largest power of 2 less than that number and put a 1 in corresponding position
Repeatedly divide the number by 2 and put the remainder from right to left
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14. Hexadecimal
Radix r = 16
Why use hexadecimal? Shorthand notation for binary
Grouping 4 bits in binary to get 1 digit in hexadecimal
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15. Binary Addition
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16. One-bit Adder
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17. 4-bit Adder
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18. Overflow
Overflow occurs when the result of an arithmetic operation is out of range and indicates an error
For example, in a computer with n-bit words, if the addition of two n-bit integers produces an (n+1)-bit result, we call it overflow
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19. Binary Coded Decimal (BCD)
Most computers operate on binary numbers
However, for computers to interface with humans, the mode of communication is generally decimal
Convert from decimal to binary on input
Convert from binary to decimal on output
But the decimal output still needs to be coded into binary, digit by digit
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20. Binary-Coded Decimal Codes
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21. Other Codes ASCII: used to transmit alphanumeric information
Gray code: consecutive numbers differ in only one bit
Particularly useful in coding the position of a continuous device and error detection
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