Ritu Ashok Gupta RAIT Navi-Mumbai rg140593@gmail. com Gayatri Katkar RAIT Navi-Mumbai gayatrigkatkar@g mail.com Snehal Kadam RAIT Navi-Mumbai snehalkadam2512 92@gmail.com Mrs. S.N. Ghate RAIT Navi-Mumbai snghate23@gmail. com

ABSTRACT

The primary advantage of XS-3 coding over BCD coding is that a decimal number can be nines' complemented (for subtraction) as easily as a binary number can be ones' complemented ; just invert all bits. In addition, when the sum of two XS-3 digits is greater than 9, the carry bit of a four bit adder will be set high. This works because, when adding two numbers that are greater or equal to zero, an "excess" value of six results in the sum. Since a four bit integer can only hold values 0 to 15, an excess of six means that any sum over nine will overflow. A code converter is a circuit that makes the two systems compatible even though each uses a different binary code. Our project is to convert a user entered BCD number into Excess-3 using 4:1 MUX. We chose to use multiplexer so as to simplify the circuit and reduce the use of more number of IC’s.

channel is displayed on your screen. Similarly, you select a radio station to listen to, and it plays on your radio. An n-1 MUX consists of the following: Data inputs: n Control inputs: ceil (log2 n) Outputs: 1 Where ceil is the ceiling function ceil(x) = n for the smallest integer where n >= x. Given n possible choices for inputs, you need log2 n bits to select it (technically, you need the ceiling of this; just in case n is not a power of 2). For example, if you have 16 possible inputs, you need 4 bits to specify one of 16 values. If you have, say, 12 possible inputs, you still need 4 bits, even though some of the 4 bit patterns may not correspond to any of the 12 choices. 4:1 MUX In electronics, a multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2n inputs has n select lines, which are used to select which input line to send to the output. Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth. A multiplexer is also called a data selector. [4] 4:1 mux will have 4 input, 1 output and 2 select lines. Block diagram, circuit diagram, truth table for 4:1 mux are shown below.

1. INTRODUCTION

Excess-3 (XS-3) code, also called biased representation or Excess-N, is a complementary BCD code and numeral system. It was used on some older computers with a prespecified number N as a biasing value. It is a way to represent values with a balanced number of positive and negative numbers. It is a non weighted code. In XS-3, numbers are represented as decimal digits, and each digit is represented by four bits as the BCD value plus 3 (the "excess" amount). To convert from binary code A to binary code B, the input lines must supply the bit combination of elements as specified by code A and the output lines must generate the corresponding bit combination of code B. BCD-to-excess-3 code converter: Each code uses four bits to represent a decimal digit Four input and four output variables are present A, B, C, D => Input variables W, X, Y, Z => Output variables 4 binary variables have 16 bit combinations, only 10 are listed in truth table, others are don’t care conditions.

2. MULTIPLEXERS

As we construct a CPU, one very useful combinational logic circuit is a multiplexer. An n-1 multiplexer, or MUX, for short, is a device that allows you to pick one of n inputs and direct it to an output. Many devices are essentially multiplexers. Think about a remote control for a TV. You select one channel, and that one Figure 1 To see if you understand condensed truth tables, let's consider a 4-1 MUX. This MUX has the following attributes: Data inputs: 4 (x3, x2 x1, x0)

Control inputs: 2 (s2, s1) Outputs: 1 (x) This time, we think...