1. Assume A and B are two 4-bit signed numbers represented in 2's complement form. Find what are the largest and smallest numbers they can represent? Create a table that show the binary and decimal equivalent of the 4-bit signed numbers. Signed Decimal Binary Representation Equivalent A3 Az A1 Ao
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Digital Logic Design
4-bit Binary Adder / Subtractor
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- 1) Answer the following questions: What is the greatest magnitude negative number one can represent in n-bit 2'scomplement code? 2)Show the 8-bit binary signed-magnitude representation for the following decimalnumbers: -109 10 +43 10 3)Perform the following additions and subtractions. Assume the numbers arestored in signed-magnitude base 2 representation. -1010111 + -100117. Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability. 1101 0110 + 1001 0111 -------------- Overflow? Yes or No Carry? Yes or No1. A CRC code uses the following generator: G = 0x225. Codewords have 8 data bits. (a) Write the binary representation of G. (b) Write the polynomial representation of G. (c) How many CRC bits are there in a codeword? (d) Calculate the corresponding codeword for the following information bits: 0010 0011. Please provide clear explanation
- 6. Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2's complement notation to decimal notation: i) 110011, ii) 001101, iii) 101101 7. Show how each of the following floating point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields): a. 12.5 b. −1.5 c. 0.75 d. 26.625 8. The following is a representation of a decimal floating value using IEEE-754 single precision. Find out the value in decimal. 0 10000011 10101000000...0Consider a 6-bit two’s complement representation. Fill in the box with question mark "?" in the following table. You don't need to care about "n/a." Number Binary Representation TMin + TMin ? Please input the binary representation in this format xxxxxx. For example, if the answer is 010010, please input 010010.2. Convert the following binary numbers to floating point format. Assume a binary format consisting of a sign bit (negative = 1), a base 2, 8-bit, excess-128 exponent, and 23 bits of mantissa, with the implied binary point to the right of the first bit of the mantissa.a. 110110.011011b. −1.1111001c. 0.1100×236d. 0.1100×2−36
- 47 by -18 (integers in decimal (base 10)). Q1 : What is the remainder of the division in FP decimal representation (i.e., if rem=53 then its FP decimal representation is 53.0)? What is the resulting number if you shift it three digits to the right of the decimal point? Express your shifted result as a single precision FP number using the IEEE 754 standard for single precision. YOU MUST FIRST CONVERT THE NUMBER FROM BASE 10 to BASE 2 and then do normalization etc. Do not calculate more than the first 8 fraction bits.1.37 Because A − B = A + (−B), the subtraction of signed numbers can be accomplished by adding the complement. Subtract each of the following pairs of 5-bit binary numbers by adding the complement of the subtrahend to the minuend. Indicate when an overflow occurs. Assume that negative numbers are represented in 1's complement. (b) 11010 −11001 (c) 10110 −01101 Repeat the question using 2's complement to represent negative numbers.Examples of 8-bit binary representations of the decimal value 30 are shown below. definition a) the opposite of a term; b) Excess-M;?
- 9. Answer the following questions about IEEE 754 32-bit single precision numbers. a. Draw a diagram of the number format. b. What’s the range of numbers that can be represented? c. What’s meant by normalization? d. What’s the implied bit? e. What’s meant by exponent overflow and underflow? f. What’s meant by significand overflow and underflow? g. How’s + ∞ represented? h. How would he following numbers be represented? i. 1.6328125 x 2^-20 ii. 1.6328125 x 2^20 iii. -1.6328125 x 2^-20 iv. -1.6328125 x 2^20Complete the following arithmetic operations in two's complement representation. What are the values of the carry and overflow flag? Assume a six-bit system. 3 + 21 = ?1. Assume numbers are represented in 8-bit two's complement Show the calculation of the following: a) 5 + 10 b) 5 – 10 c) -5 + 10 d)-5 – 10 2. Represent the following decimal numbers or values according to the given requirements: a) +4 in both binary sign/magnitude and two's complement b) -6 in both binary sign/magnitude and two's complement c) -85 in two's complement d) +52 in two's complement 3. Find the following differences using twos complement arithmetic: a) 001000 – 110111 b) 10100101 – 011110 c) 100100001011 – 101010110011 d) 10011011 – 10100101