Let g(x) be a function so that the following covariance and
expectations are finite numbers. Show that
cov [g(U), g(1 − U)] = (1/2) E {[g(U1) − g(U2)][g(1 − U1) − g(1
− U2)]} ,
where U ∼ U(0, 1), U1 and U2 are iid U(0, 1). Note you need the
fact about the independences of U1 & 1 − U2 as well as 1 − U1
& U2 to show the above identity.
1) Covert the following binary values to decimal. Do this
interpreting the binary as unsigned and signed.
a. 0111 1001
b. 1000 0000
c. 1111 1111
PLEASE EXPLAIN IT IN DETAIL
Convert the following unsigned numbers
to the requested form:
01100001 binary to: hex, and also decimal
Hex:
Decimal:
b) 136 decimal to: hex, and also binary
Hex:
Binary:
) Subtract the following numbers in binary:
(i) 2576310 – 245410 (ii) 983210 – 243210 (iii) 450610 – 200410
(iv)
900610 – 459810 (AN 4marks)
(ii)Express the following hexadecimal numbers to their
equivalent
binary and octal numbers. (i) 3AC45B.20B (ii) 6754A.2FE (iii)
4596BC.31DF (iv) 2369.2AB7 ( AN 4marks)
(c) What is the range of unsigned and signed decimal numbers as
well
as binary numbers that can be represented in a 10 bit system
Make the following assumptions: Assume a binary search tree
holds integer numbers Write a pseudocode for a binary tree search
algorithm that searches in the tree (starting at root) for a node
which meets the following requirements, and prints a message when
found:
(a) has a value that is one third as large as either its left or
right child node. Think carefully about what steps are needed to do
the search, and review the insert and search methods for...
7 – For the following operations:
• write the operands as 4-bit 2's complement binary numbers,
• perform the operation shown,
• show all work in binary operating on 4-bit numbers, and
• identify overflow if necessary.
a) 4 + 2
b) 4 – 2
c) 2 – 4
d) 4 + 4
Perform double dabble on the following binary (base 2) numbers:
Please show your work for full credit. Either digital or hand
written is fine.
1. 10011010010
2. 101010
3. 100111010
4. 10101001101
5. 1100100000
For 10pt extra credit - write a program that implements the
double dabble algorithm.
Convert the following numbers to 32-bit, 2s compliment binary
and hexadecimal formats. Show your work in recursive division form.
899726616
1656906428
-77102817
-251026154