270
Introduction ECE to Digital System Design
Fall 2011
TakeHomaWork for Module 5 Due November 2, 2011
1. [2 points] Unsigned conversion: (2C9E)16 to base 2 (0010 1001 1100 1110)2
2. [2 points] Unsigned conversion: (1101001)2 to base 10 (105)10
3. [2 points] Unsigned conversion: (1101001)2 to base 16
(69)16
4. [2 points] Unsigned conversion: (8576)10 to base 16 (2180)16
5. [12 points] Signed conversions: R( 0 1 0 0 0 1 )2 SM( 0 1 0 0 0 1 )2 DR( 0 1 0 0 0 1 )2
DR( 1 0 1 1 1 0 )2
R( 1 0 1 1 1 1 )2
SM( 1 1 0 0 0 1 )2
SM( 1 0 1 1 1 0 )2
DR( 1 1 0 0 0 1 )2
R( 1 1 0 0 1 0 )2
ECE 270
Introduction to Digital System Design
Fall 2011
TakeHomaWork for Module 5 Due November 4, 2011
1. [8 points] Radix addition (base 2)
1 0 0 1 1 + 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 + 1 0 0 1 1 0 0 1 1 0
OVF
0 1 1 1 1 + 1 0 0 0 0 1 1 1 1 1
0 1 1 1 1 + 0 1 0 1 0 1 1 0 0 1
OVF
2. [12 points] Radix subtraction (base 2)
1 0 0 0 1 - 1 1 1 1 1 1 0 0 1 0
1 0 0 0 0 - 0 1 0 1 1 0 0 1 0 1
OVF
0 1 0 1 1 - 0 0 0 0 0 0 1 0 1 1
0 1 0 1 1 - 1 0 0 0 1 1 1 0 1 0
OVF
ECE 270
Introduction to Digital System Design
Fall 2011
3. [10 points] Tired of writing the names of those you want "kicked off the island" on cards, you wish to modernize the voting scheme used on Digital Survivor. Specifically, you would like to design a circuit that tabulates the "stay on the island"/"kick off the island" (yes/no) votes of up to 7 fellow contestants. Armed with only a bucket of full-adder cells (plus 7 switches, some resistors, 3 LEDs, a breadboard, some wires, a battery, and a large pepperoni pizza), you start your Amazing Digital Race. Assume the tribunal can correctly interpret 3-bit binary numbers. HINT: This is sometimes called a "population counting" circuit here we simply want to tabulate the number of inputs that are "1".
V1 V2
X
CS
Y Z
V3
V4
X
CS
Y Z
V5
V6
X
CS
S2 S1
Y Z
X
CS
S0
Y Z
V7
ECE 270
Introduction to Digital System Design
Fall 2011
TakeHomaWork for Module 5 Due November 7, 2011
1. [36 points] Determine how the condition codes (C, Z, N, V) are set for 2-bit Radix
subtraction. Show all work. 1 0 - 0 1 _____ 0 1 1 0 - 1 0 ______ 0 0 1 0 - 1 1 _____ 1 1
C = 0 N = 0 0 1 - 0 1 _____ 0 0
Z = 0 V = 1
C = 0 N = 0 0 1 - 1 0 _____ 1 1
Z = 1 V = 0
C = 1 N = 1 0 1 - 1 1 _____ 1 0
Z = 0 V = 0
C = 0 N = 0 0 0 - 0 1 _____ 1 1
Z = 1 V = 0
C = 1 N = 1 0 0 - 1 0 _____ 1 0
Z = 0 V = 1
C = 1 N = 1 0 0 - 1 1 _____ 0 1
Z = 0 V = 1
C = 1 N = 1
Z = 0 V = 0
C = 1 N = 1
Z = 0 V = 1
C = 1 N = 0
Z = 0 V = 0
ECE 270
Introduction to Digital System Design
Fall 2011
2. [14 points] Complete the missing entries in the "condition code generation chart," below, and derive the function for "A greater than or equal to B" ("AGEB") in its simplest (minimal) form. Show all work. A1 (A) A0 B1 B0 (B) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 +1 +1 +1 [phone] 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ? C Z N V
(A) = (B) 0 1 0 0
+1 (A) < (B) 1 0 1 0 -2 (A) > (B) 1 0 1 1 -1 (A) > (B) 1 0 0 0 0 (A) > (B) 0 0 0 0 +1 (A) = (B) 0 1 0 0 -2 (A) > (B) 1 0 1 1 -1 (A) > (B) 1 0 1 1 0 (A) < (B) 0 0 1 0 +1 (A) < (B) 0 0 0 1 -2 (A) = (B) 0 1 0 0 -1 (A) < (B) 1 0 1 0 0 (A) < (B) 0 0 1 0 +1 (A) < (B) 0 0 1 0 -2 (A) > (B) 0 0 0 0 -1 (A) = (B) 0 1 0 0
AGEB = (NV)
ECE 270
Introduction to Digital System Design
Fall 2011
TakeHomaWork for Module 5 Due November 9, 2011
1. [20 points] Compile the ABEL program (listed below) using ispLever in order to determine the minimum number of P-terms required for the code as written. Attach a copy of the Reduced Equation report to document your answers.
MODULE cla4 TITLE '4-bit Carry Look-Ahead Adder for 26V12' DECLARATIONS X0..X3, Y0..Y3 pin; " operands CIN pin; " carry in S0..S3 pin istype 'com'; " sum outputs C0..C3 pin istype 'com'; " carry outputs (C3 is carry out) G0..G3 pin istype 'com'; " generate functions P0 P1 P2 P3 = = = = X0$Y0; X1$Y1; X2$Y2; X3$Y3; " propagate functions
EQUATIONS G0 G1 G2 G3 = = = = X0&Y0; X1&Y1; X2&Y2; X3&Y3; " generate functions
" carry functions C0 = G0 # CIN&P0; C1 = G1 # G0&P1 # CIN&P0&P1; C2 = G2 # G1&P2 # G0&P1&P2 # CIN&P0&P1&P2; C3 = G3 # G2&P3 # G1&P2&P3 # G0&P1&P2&P3 # CIN&P0&P1&P2&P3; S0 S1 S2 S3 END = = = = CIN$P0; C0$P1; C1$P2; C2$P3; " sum bit outputs
Number of P-terms required to implement equation for C0 = 3 Number of P-terms required to implement equation for C1 = 5 Number of P-terms required to implement equation for C2 = 7 Number of P-terms required to implement equation for C3 = 9 Number of P-terms required to implement equation for Si = 4
ECE 270
Introduction to Digital System Design
Fall 2011
2. [20 points] Draw a circuit that multiplies a 4-bit unsigned binary number X3 X2 X1 X0 by a 3-bit unsigned binary number Y2 Y1 Y0, using an array of full-adder cells. Determine the worst case propagation delay if each full adder takes 10 ns to produce its C and S outputs, and each AND gate (used to generate the product components) has 10 ns of propagation delay. X3 X2 Y2 X1 Y1 X0 Y0
X
X3Y0 X2Y0 X1Y0 X0Y0 X3Y1 X2Y1 X1Y1 X0Y1 X3Y2 X2Y2 X1Y2 X0Y2 P6 P5 P4 P3 P2 P1 P0
CS
Y Z
full adder cell to use
Array should have 3 diagonals/3 rows (9 FA cells total, plus 12 AND gates); worst case delay path is 60 ns
X3Y0 X2Y1
X
X2Y0 X1Y1
X Y Z
X1Y0
X
X0Y0 X0Y0 X0Y1 0
CS
X3Y1
X X Y Z
Y Z
X1Y2 C
0
S
CS
Y Z
CS
X3Y2
X
X2Y2 C
S
Y Z
X
0
CS
Y Z
X0Y2
CS
P6
Y Z
X
CS
Y Z
X
CS
Y Z
0
P5
P4
P3
P2
P1
P0