1. Find the decimal equivalent of the following binary numbers expressed in the 2's complement format: a) 00001110 b) 10001110 2. Using Boolean algebra, simplify the expression: F= XZ+ X(Y+Z) + Z(Y +Z) 3. Find the binary equivalent of (374.26)s and the octal equivalent of (1110100.0100111)2
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- 23. The binary number 101110101111010 can be written in octal as a. 515628 b. 565778 c. 656278 d. 5657281. Convert the following decimal numerals to their binary, octal and hexadecimal equivalents (in case of infinite extension, compute the first 10 digits after dot): a. 55438, b. 237170, c. 586.609375 d. 22.016845703125 e. 416.712 2. Convert (416.715); to its decimal, binary, and hexadecimal equivalent 3. Find appropriate numeral system base, for which given equation is correct: a. 12,1 = 302/20 b. 41/3 = 13 c. 23+44+14+32 = 223 4. Find 8-bit l's complement numerals representing the following decimal numerals: a. 89 b. 135 c. 225 d. -37 e. -78 f. -128 g. -230 5. Repeat task 4, this time searching for 2's complement numerals 6. Compute: a. 11100 + 10001 b. 11100 + 00100 c. 01100 - 10011 assuming (one-by-one): signed-magnitude, l's complement, 2's complement representationExercises : Convert the following binary numbers to Hexadecimal numbers: (b) 1100111010002 (a)11001010010101112 (c) 101010. 101012 (d) 1111110001.011010012 0110111012 (e) 1011001110. Answers:
- Q1/The binary number ( 1011011011011.1110111001101)= ( ) in octal number *Perform the addition of the following 8-bit 2's complement numbers using 2's complement arithmetic. (Reminder: 2's complement numbers are signed numbers.) a) 11001001 + 00110011 b) 10011011 + 01101111 c) 01011010 + 10110110 d) 11001000 + 11100101 Convert each result from the previous problem to signed decimal. Draw the block diagram of the circuit required to implement the operation in Problem 3.IH.W: Draw a logic eircuit of the following Boolean expression before and after simplification using karnough map and Boolean expression. Y-AB+ AB A B Y 1 1
- Computer architecture 1. Perform the following calculations. All numbers are 8-bit Integers; except where noted. Show all work. Note any overflow. Note that 2c signifies 2s complement and sm signifies signed-magnitude. I suggest you check your answers in base 10. 11110110 - 100101112c= 11110110 & 00001111= Convert -1610sm to Base 16 Convert AD16c to Base 10 F9 + E916c=The number 7357.68K represented in engineering notation can also be represented as Select one: O a. 735768M b. 7357680m c. None of these d. 7357.68MThe binary string 11010111100101 is a floating-point number expressed using the 14-bit simple model given in your text. What is its decimal equivalent? Note: in the 14-bit simple model, the left-most bit is the sign, followed by 5 bits for the exponent, followed by 8 bits for the mantissa (There are no implied bits). The exponent is in Excess 15 notation.
- Convert the following binary numbers to hexadecimal without using a calculator (show work where nibbles are identified). a. 1110.0101 b. 1010010.01001 c. 1100.010001 d. 1000.11001010111(m. Simplify the given expression using Boolean algebra and implement the simphifie expression using basic logic gates. Y = A.B.C+ A.B.C + A.B.C + A.B.CConvert the following binary numbers to decimal form: (show your work) (110011.11)2 (1000001.111)2 (1011100.10101)2