Company LOGO DKT 1223 DIGITAL SYSTEM 1 E

Company LOGO DKT 122/3 DIGITAL SYSTEM 1 E d i t y o u r s l o g a n h e r e WEEK #11 FUNCTIONS OF COMBINATIONAL LOGIC (PART 4)

Topic Outlines Company LOGO Code Converters Ü Comparators Ü Parity Generators/Checkers Ü

Code Converters Company LOGO Ü Code converters is a device that is used to convert a coded number into another form that is more usable by a computer or digital system Ü Example: BCD to binary, BCD to 7 segment display, Gray-to-binary code and binary-to-Gray code

Code Converters Company LOGO BCD-to-Binary Conversion The basic conversion process is as follows: (a) The value, or weight of each bit in the BCD number is represented by a binary number (b) All of the binary representations of the weights of bits that are 1’s in the BCD number are added (c) The result of this addition is the binary equivalent of the BCD number

Code Converters Company LOGO BCD-to-Binary Conversion Example: weight 1000 0111 8 7 10 1 : BCD : decimal Within each group, the binary weight of each bit is as follows: Weight: Bit designation: Tens Digit 80 40 20 10 B 3 B 2 B 1 B 0 Units Digit 8 4 2 1 A 3 A 2 A 1 A 0

Code Converters Company LOGO BCD-to-Binary Conversion BCD BIT BCD WEIGHT BINARY REPRESENTATION (MSB) (LSB) 64 32 16 8 4 2 1 A 0 1 0 0 0 0 A 1 2 0 0 0 1 0 A 2 4 0 0 1 0 0 A 3 8 0 0 0 1 0 0 0 B 0 10 0 1 0 B 1 20 0 0 1 0 0 B 2 40 0 1 0 0 0 B 3 80 1 0 0 If the binary representations for the weights of all the 1’s in the BCD number are added, the results is the binary number that corresponds to the BCD number.

Code Converters Company LOGO Binary-to-Gray Conversion (and vice-versa) 4 -bit binary-to-Gray conversion logic 4 -bit Gray-to-binary conversion logic

Comparators Company LOGO Ü To compare two digital quantities to determine the relationship of those quantities Ü Comparison is made in terms of Ü Equal to (“=”) Ü Less than (“<”) Ü Greater than (“>”)

Comparators Company LOGO Equality Truth-Table A B A=B 0 0 1 0 1 0 0 1 1 1 The output of the AND gate indicates equality (1) or inequality (0) Logic diagram Equality comparison of two 2 -bit numbers

Comparators Company LOGO Inequality (“<” or “>”) To determine the inequality of binary numbers A and B, first examine the highest order bit for each number: Ü If A 3=1 and B 3=0, means number A > B Ü If A 3=0 and B 3=1, means number A < B Logic symbol for a 4 -bit comparator with inequality function Ü If A 3=B 3, need to examine the next lower bit position for an inequality

Comparators Company LOGO 7485 comparator chip

Comparators Company LOGO 8 -bit magnitude comparator

Parity Generators/Checkers Company LOGO Error detection Ü A parity bit is a scheme for detecting errors during transmission of binary info. Ü The message, including the parity bit, is transmitted and then checked at the receiving end for errors. Ü An error is detected if the checked parity does not correspond to the one transmitted. Ü The circuit that generates the parity bit in the transmitter is a parity generator. Ü The circuit that checks the parity bit in the receiver is a parity checker.

Parity Generators/Checkers Company LOGO Error detection Ü Parity systems are defined as either odd parity or even parity. Ü The parity system adds an extra bit to the digital information being transmitted. Ü E. g. : 4 -bit system requires a 5 -th bit, 8 -bit system will require a 9 -th bit, … Ü The parity bit will be a 1 or 0, depending on what the other bits are. Ü E. g. (4 -bit system) Odd-parity system - the parity bit that is added must make the sum of all 5 bits odd Even-parity system - the parity bit makes the sum of all 5 bits even

Odd Parity Company LOGO In ODD parity when we add the bits together disregarding weight we get or want to get an odd number. 0000 is a four bit message Parity bit add a parity bit to make it odd 10000 00011001 000011001 Odd parity is satisfied is an eight bit message add a parity bit to make it odd Odd parity is satisfied

Even Parity Company LOGO In EVEN parity when we add the bits together disregarding weight we get or want to get an even number. 0000 is a four bit message Parity bit add a parity bit to make it even 00000 00011001 100011001 Even parity is satisfied is an eight bit message add a parity bit to make it even Even parity is satisfied

Parity Generator Company LOGO Parity Generator Use exclusive ORs and Exclusive NORs Even Parity Odd Parity

Parity Generator Company LOGO Parity generator truth table For odd parity, the bit P is generated so as to make the number of 1’s odd (including P) X Y Z P 0 0 0 1 0 0 0 1 1 1 1 0 3 -bit odd parity generator Question: How about EVEN parity generator?

Parity Checker Company LOGO Parity Checker 0 – ok 1 – error Even Parity Odd Parity

Parity Checker Company LOGO The three-bit message (X, Y, Z) and parity bit (P) are transmitted to their destination, where they are applied to a ODD parity checker circuit. Ü An error occurs during transmission if the parity of the four bits is even, since the binary info transmitted was originally odd. Ü The output C of the parity checker should be a 1 when an error occurs, i. e. when the number of 1’s in the four inputs is even. Ü X 0 0 0 0 1 1 1 1 Y 0 0 0 0 1 1 1 1 Z 0 0 1 1 P 0 1 0 1 C 1 0 0 1 1 0 0 1

Parity Generators/Checkers Company LOGO The 9 -bit parity generator/checker Input is 8 -bits of data and 1 parity bit When there is an even no. of 1’s at the inputs, the Σ Even is high while the Σ Odd is low.

Parity Generators/Checkers Company LOGO The 9 -bit parity generator/checker Parity Checker Function Ü When used as an EVEN Parity Checker, If a parity error occurs, the Σ Even is low while the Σ Odd is high. Ü When used as an ODD Parity Checker, If a parity error occurs, the Σ Odd is low while the Σ Even is high.

Parity Generators/Checkers Company LOGO The 9 -bit parity generator/checker Parity Generator Function Ü When used as an EVEN Parity Generator, The parity bit is taken at the Σ Odd output. Ü It is 0 if there is an even no. of 1’s, and is 1 if there is an odd no. Ü When used as an ODD Parity Generator, The parity bit is taken at the Σ Even output. Ü It is 0 if there is an odd no. of 1’s, and is 1 if there is an even no. E D N