cpe midterm

What are the relationships between binary octal and hexa?

•Each octal digit corresponds to 3 binary digits •Each hexa digit corresponds to 4 binary digits

Octal(Hexa)-Binary Conversion? Perform on 1234(octal) and C0DE(hexa)

•Octal: substitute each digit with its 3-digit binary equivalent Answer = 001010011100 •Hexa: substitute each digit with its 4-digit binary equivalent Answer = 1100000011011110

Binary to Hexa conversion? Perform on (10111011001. 111100000110)

•Partition the binary number into groups of four digits each, starting from the binary point, going right and left Answer = 5D9.F06

Binary to Octal conversion? Perform on (10111011001.111100000110)

•Partition the binary number into groups of three digits each, starting from the binary point, going right and left Answer = 2731.7406

Digital has _____ possible values.

finite

Analog signal has _____ possible values.

infinite

How to decimal to octal/hexa conversion? Perform octal conversion on 467, and perform hexa conversion on 3417.

Operation is the same as binary but divide by 8 and 16 respectively. Answer = 723 Answer = D59

Given numbers: X = 40, Y = 27. 1) Express X, -X, Y, -Y in signed 2's complement form. 2) Perform X-Y in signed 2's complement form.

1) 0101000, 1011000, 0011011, 1100101 2) 10001101. There was overflow because ...

How to convert from decimal to binary? Perform on 179

1) Divide the number by 2 -> quotient + remainder 2) Divide all successive quotients by 2 and record the remainders 3) Take the remainders in reverse order (end to beginning) -> binary number Answer = 10110011

How to decimal to binary conversion (Radix Point)? Perform on 0.6875

1) Multiply the number by 2 -> integer and fraction 2) Multiply the successive fractions by 2 and record the integer values. 3) When the fraction becomes 0, take the integers in order (beginning to end) -> binary number Answer = 0.1011

Given function: F(x,y,z) = x'yz + x'yz' + yz + x'y'z' 1) Draw the K-map 2) Express the simplest form of F in sum-of-products form. 3) Draw a two level NAND implementation of the resulting function

1) See last yr's test 2) F = x'z' + yz 3) See last yr's test

Convert to decimal: 1110₂

14

Convert to octal: 11010₂

1A

Convert to base 5: 71₁₀

241

How many numbers can we represent with "n" bits? Perform on 3 digits with base 10

2ⁿ numbers, in range from 0 to 2ⁿ-1. General base case: with n digits in base r: rⁿ numbers, in range 0 to rⁿ-1.

Convert the decimal number 52 to binary and octal representations. Show work.

Binary: 110100 Octal: 64

A decoder with 3 inputs has 4 output lines. (T/F)?

False

Perform two level logic size minimization for the function F(x,y,z) = x'yz + x'yz' + yz + x'y'z' if it is known that combination 100 and 110 can never occur. Express in sum-of-products form.

See last yr's test for kmap. F = y + z'`

Convert the 5 bits binary number 11011 in the following three systems: signed 1's complement, signed 2's complement, signed magnitude. Express the decimal value of the number for these representations.

Signed 1's complement: -4 Signed 2's complement: -5 Signed magnitude: -11

A digitized signal is easier to recover at a receiver than an analog signal (T/F)?

True

By using 2's complement form it becomes possible to eliminate the need for designing a separate subtractor circuit. (T/F)?

True

Function F(a,b) = ab + a'b + a'b' is in sum-of-minterms form. (T/F)?

True

Make a truth table for the following function and then draw the logic circuit. G(x,y,z) = xz + 0 + (x' + y')(x + z)

Truth table: x y z F 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 Logic Circuit: See Jeremy's cpe quiz page 5

How to decimal to octal (Radix Point)? Perform on 0.513 to 6 floating points.

Use multiplication method, by 8. Answer = 0.406517

How to convert from binary to decimal?

add the coefficients multiplied by the powers