# Lec05 - 1 ECE 212 Digital Circuits II Monday 9 February...

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Unformatted text preview: 1 ECE 212 Digital Circuits II Monday, 9 February 2008 Â¡ HW Set 5: â€¢ Problem 1 Laura P. â€¢ Problem 2 Rob S. â€¢ Problem 3 NO PRESENTER â€¢ Problem 4 Sheena S. â€¢ Problem 5 Dan S. â€¢ Problem 6 Colin T. â€¢ Problem 7 Ben T. â€¢ Problem 8 NO PRESENTER Today's Goals Â¡ To understand how to represent signed intgers using two's complement notation. Â¡ To understand how to perform mathematical operations on signed numbers that are represented in two's complement notation. â€¢ Multiplication by 2. â€¢ Division by 2. â€¢ Addition. Â¡ To understand arithmetic overflow. 2 4-bit Two's Complement Representation N b3 b2 b1 b0 +7 0 1 1 1 +6 0 1 1 +1 0 0 0 1 0 0 0 0 â€“ 1 1 1 1 1 â€“ 2 1 1 1 â€“ 7 1 0 0 1 . . . . . . . . . . . . +2 0 0 1 â€“ 6 1 0 1 â€“ 8 1 0 0 1 2 4 â€“ 8 Bit Weights: b3 b2 b1 b0 interpreted as pure binary 7 6 . . . 2 1 15 14 . . . 10 9 8 = 16 â€“ 1 = 16 â€“ 2 = 16 â€“ 6 = 16 â€“ 7 = 16 â€“ 8 Complement with respect to 16 = 2 4 . Sign Bit Extension (1/2) Problem: Design a combinational circuit: Inputs: x3 x2 x1 x0 The 4-bit, 2's complement representation for N. Outputs: z7 z6 z5 z4 z3 z2 z1 z0 The 8-bit, 2's complement representation for the same integer N. Examples: â€“ 6 â‡” 1 0 1 â€“ 128 64 32 16 8 4 2 1 â€“ 6 â‡” + 3 â‡” 0 0 1 1 + 3 â‡” 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 â€“8 4 2 1 3 Sign Bit Extension (1/2) Problem: Design a combinational circuit: Inputs: x3 x2 x1 x0 The 4-bit, 2's complement representation for N....
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Lec05 - 1 ECE 212 Digital Circuits II Monday 9 February...

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