Hw23_SLN - ECE 211 HW 23 SOLUTIONS p 1 of 12 C\ECE211\HW\hw23(BinAdd\hw23_SLN HW Set 23 SOLUTIONS 1 A combinational circuit to increment a 3-bit

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ECE 211 HW 23 SOLUTIONS p 1 of 12 //home/vdimitrov/8932/f16cdc8711318782bff26ccf8bf525b86d00e336.doc HW Set 23 SOLUTIONS 1. A combinational circuit to increment a 3-bit number has the following specifications: Inputs: x2 x1 x0, the bits of the 3-bit number (all active-High). Outputs: z2 z1 z0, the bits of the output number (all active-High); Error (active-High). Operation: Let X = the input number, Z equal the output number. The circuit operation is Z = X plus 1. If the incremented result cannot fit into 3 bits, then Error = 1; otherwise, Error = 0. Solution: (a) Design this circuit using Half Adders. x2 x1 x0 + 1 z2 z1 z0 (b) Design this circuit by: (i) Completing this Truth Table. x2 x1 x0 z2 z1 z0 Error 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 d d d 1
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ECE 211 HW 23 SOLUTIONS p 2 of 12 (1. ) (ii) Writing minimal sum-of-product expressions for z2, z1, z0, Error. (You need not realize your expressions with logic gates.) z2 = x2 + ( x1 · x0 ) z1 = ( x1 · x0 ' ) + ( x1' · x0 ) = x1 x0 z0 = x0 ' From the Truth Table, Error = x2 · x1 · x0
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ECE 211 HW 23 SOLUTIONS p 3 of 12 2. Construct a State Transition Diagram for a Mealy circuit: Input: x Outputs: z, Error Operation: The circuit processes the input in non-overlapping 3-bit blocks. Each 3 bits are interpreted as a binary number; the first bit in the block is the least significant bit. The output z gives the 3 bits of the input number plus one. If the incremented result does not fit into three bits, then Error = 1; otherwise Error = 0. An input-output example is: x = 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 z = 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 Error = 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 Solution: The State Transition Diagram must keep track of: 1. The number of bits received. 2. Whether there is a carry or not.
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This homework help was uploaded on 04/17/2008 for the course ECE 211 taught by Professor Nestor during the Fall '07 term at Lafayette.

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Hw23_SLN - ECE 211 HW 23 SOLUTIONS p 1 of 12 C\ECE211\HW\hw23(BinAdd\hw23_SLN HW Set 23 SOLUTIONS 1 A combinational circuit to increment a 3-bit

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