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Sample_Midterm_sol

# Sample_Midterm_sol - EE 101 Sample Midterm Redekopp Name...

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1 EE 101 Sample Midterm Redekopp Name:_________________________________________________________________ Score: / 100 1. Short Answer (5 pts.) a. What range of numbers can be represented with a 6- bit 2’s complement system? -2 n-1 to +2 n-1 -1 = -32 to +31 b. What are the three primary design goals that we try to optimize in circuit design? 1.) Area or Size 2.) Speed or Delay 3.) Power c. Given a 5-to-32 decoder with inputs (A4, A3, A2, A1, A0), write out the logic equation for output 17 (i.e. O17)? 17 = 10001 2 = A4 •A3’ •A2’ •A1’ •A0 d. NAND-OR logic implementations degenerates to what gate? NAND e. A 20-to-1 mux would require a minimum of how many select bits? 5 bits 2. For the decimal numbers below, convert to the indicated representation systems. a. (-107) 10 = (?) 8-bit 2’s comp. = (?) 16 ’s comp. (i.e. just conv. 2’s comp. value to hex) (4 pts.) -107 = 10010101 2’s comp = 95 16’s comp b. (-59) 10 = (?) 8-bit signed magnitude (2 pts.) -59 = 10111011 8-bit signed mag. c. 235 10 = (?) 8 = (?) BCD (6 pts.) 235 / 8 = 29 r. 3 29/8 = 3 r. 5 3/8 = 0 r. 3 = 353 8 235 = 0010 0011 0101 BCD

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2 3. Find the simplest SOP form of the following logic equation. (8 pts.) C AB C C A B C A F ] ) ( ) [( F = ((AC’)+B)((AC’)+C) + ABC’ DeMorgan’s = A C’ + BC + ABC’ T8’ = AC’ + BC Single-Variable Theorems (T1) X + 0 = X (T1’) X • 1 = X (Identities) (T2) X + 1 = 1 (T2’) X • 0 = 0 (Null elements) (T3) X + X = X (T3’) X • X = X (Idempotency) (T4) (X’)’ = X (Involution) (T5) X + X’ = 1 (T5’) X • X’ = 0 (Complement) Two- and Three-Variable Theorems (T6) X +Y = Y + X (T6’) X • Y = Y • X (Commutativity) (T7) (X+Y)+Z = X+(Y+Z) (T7’) (X•Y) •Z = X• (Y•Z) (Associativity) (T8) X•(Y+Z) = X•Y + X •Z (T8’) X+(Y•Z) = (X+Y) • ( X+Z) (Distributivity) (T9) X + X•Y = X (T9’) X • (X + Y) = X (Covering) (T10) X•Y + X•Y’ = X (T10’) (X+Y) • (X+Y’) = X (Combining) (T11) X•Y+X’•Z+Y•Z = X•Y+X’Z (T11’) (X+Y)•(X’+Z)•(Y+Z) = (X+Y)•(X’+Z) (Consensus) DeMorgan’s Theorem ( X • Y )’ = X’ + Y’ (T6’) (X +Y )’ = X’ • Y’ ( DeMorgan’s )
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