SFU - CMPT 150 - Lectures - Week 6

SFU - CMPT 150 - Lectures - Week 6 - c A.H.Dixon CMPT 150:...

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Unformatted text preview: c A.H.Dixon CMPT 150: Week 6 (Feb 11 - 15, 2008) 38 16 DEMULTIPLEXERS Whereas the multiplexer selects an input port whose value is to be delivered to the output port, the demultiplexer selects which output port to deliver the value on its single data input port. The demultiplexer is defined by the following behavioraly description: m1 = d*s1*s0 m2 s1 s0 d m0 m1 m3 m0 = d*s1*s0 m3 = d*s1*s0 m2 = d*s1*s0 The control inputs s1 and s0 determine the output port where the input will be delivered. When d is set permanently to the value 1 then the device is more commonly as a 2 4 Decoder. In particular, note that the Boolean functions that define each output correspond to all possible minterms that can be defined with literals s1 and s0 . For this reason the decoder is sometimes called a minterm generator. LIke the multiplexer, the demultiplexer is a type of digital switch. However, when configured as a decoder, it can be used to represent any sum of minterms representation where the number of variables of the function matches the number of select inputs of the decoder. That is, for a function of n variables, an n 2 n decoder is required. For example, to implement the function f ( x,y ) = m (0 , 1 , 3) a 2 4 decoder is used, along with an OR gate (see next page). The decoder is used to define all the minterms, then those minterms that are required for the given function are simply ORed together. c A.H.Dixon CMPT 150: Week 6 (Feb 11 - 15, 2008) 39 y m2 s1 s0 d m0 m1 m3 1 x More importantly, a set of functions of n variables can be implement using just one n 2 n decoder. All that is required is an OR gate to combine the minterms of each function. For example, consider the design of a circuit to add three 1-bit values. Its behavioral description is given by: c0 x s y c1 x y c1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 s c0 From the sum of minterms representations, a logic diagram can be obtained im- mediately, using a 3 8 decoder, since there are three inputs: c 1 = m (3 , 5 , 6 , 7) s = m (1 , 2 , 4 , 7) c1 s2 s1 d 1 x y c0 s0 m7 m6 m5 m4 m3 m2 m1 m0 s c A.H.Dixon CMPT 150: Week 6 (Feb 11 - 15, 2008) 40 17 UNSIGNED ADDITION The circuit to add three 1-bit values obtained in the previous section is commonly called a 1-bit full adder (FA for short). This component is a basic building block of most arithmetic circuits, including larger adders. The behavioral description for a 4-bit full adder is: (c4,s3,s2,s1,s0) = (x3,x2,x1,x0) plus (y3,y2,y1,y0) plus c0 xo y0 c0 c4 s0 y3 y2 y1 x3 x2 x1 s3 s2 s1 FA Observe that it is the sum of two 4-bit values x 3 x 2 x 1 x and y 3 y 2 y 1 y and one 1-bit value c 0. Since the sum of two 4-bit value can produce a result that requires five bits to represent it, there are five output bits; s is the least significant bit and c 4 is the most significant bit of the sum....
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This note was uploaded on 06/20/2010 for the course CMPT 150 taught by Professor Dr.anthonydixon during the Spring '08 term at Simon Fraser.

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SFU - CMPT 150 - Lectures - Week 6 - c A.H.Dixon CMPT 150:...

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