ECE-C451 Computer Arithmetic
Fall term 2010
Homework #7 Solution
1. Given A = (E5)16 and B = (F2)16
Perform the multiplication A x B using the following algorithms:
a.
Shiftleft A. B Firstversion
b.
Shiftleft A. Shiftright B
Secondversion
c. Booths Algor
ECE-C451 Computer Arithmetic
Fall Term 2010
Quiz #6
1. Consider a full decimal adder using a two-level design: first OR, then AND. Its
two inputs are two BCD digits (X and Y) and a carry (Cin). How many dont
care are there in the truth table for the circu
ECE-C451 Computer Arithmetic
Fall Term 2004
Quiz #2 Version 2
Name: _
Date: _
1. Give the truth table for a RS flip-flop. Derive a characteristic equation showing
how the next state depends on the input(s) and present state.
R
0
0
0
0
1
1
1
1
S
0
0
1
1
0
ECE-C451 Computer Arithmetic
Fall Term 2004
Quiz #2 Version 1
Name: _
Date: _
1. Give the truth table for a T flip-flop. Derive a characteristic equation showing
how the next state depends on the input(s) and present state.
T
0
0
1
1
Q (present state)
0
1
(2)
1.
Complements. Consider a positional m digit integer number system in radix r.
a) Let r = 6, m = 2. Take a number A6: (a1 ao)6 an adopt the following
notation.
If A6 2 0, denote it A6 = (O a, ao)6
If A6 < 0, denote it A6 = (5 a1 a0)6
§how by co
ECEC 451 Fall 2010
Homework Assignment 04
Solutions
1) Consider 4-digit binary arithmetic (m = 4). Find the space and time complexity of the
following circuits:
a) Ones complement generation
Assuming the circuit in Figure 2 of Handout #0
Space Complexity
ECE-C451 Computer Arithmetic
Fall term 2010
Homework #3 Solution
1. a. Perform the following additions/subtractions in binary with twos complement.
For each of these operations, simply follow the rules for twos complement
arithmetic. All numbers given are
ECEC 451 Computer Arithmetic
Fall 2010
Homework Assignment 2
Due Thursday Oct. 14th in class
1. Given a clocked SR flip-flop (see below), complete the timing diagram with the signals
for Q and Q. Assume that the flip flop is initially reset.
2. Given an e
ECE-C451 Computer Arithmetic
Fall term 2010
Homework #1
Due in class on Thursday, October 7
1. Simplify f ( x, y, z, w) w xz w xyz wxy wxy
w x( z yz ) wxy wx y
w x( z y ) wxy wx y
w xz w xy wxy wx y
xy ( w w) w xz wx y
xy w xz wx y
_
_
_
_
2. Simplif
ECE-C451 Computer Arithmetic
Fall term 2010
Homework #6 Solution
Design a circuit to perform algebraic addition of integers in sign and 2s complement format.
Subtraction (i.e., addition of a negative number) should be replaced by the adding of the 2s
comp
Quiz 1 - Version 2
ECEC451 - Prof. Trachtenberg
1.
Reduce the following to a minimum sum of products form (3 terms, 6 literals).
abc + a + abc + abc
bc
= abc + a + (bc + abc)
bc
a
= abc + a + bc
bc
= abc + c(b + )
ba
= abc + c(b + a)
= abc + bc + ac
= a(
Quiz 1 - Version 1
ECEC451 - Prof. Trachtenberg
1.
Reduce the following to a minimum sum of products form (2 terms, 3 literals).
xy z + xy z + xyz + xy z + xyz
Associative
Ident (a + a) = 1
Distributive
Simplication: a + ab = a + b
Distributive
Ident (a