Find the representation x of the following numbers listed below in the base specified on the right; 1.- (10100110)2=(x)10 # both signed and unsigned for a eight-bit binary representation 2.- (207)10=(x)2 3.- (-135)10=(x)2 # In a two-complement representation 4.- (2D7)16=(x)2 5.- (-3.3125)10=(x)2 #IEEE 754 standard, 32 bit representation
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1.- (10100110)2=(x)10 # both signed and unsigned for a eight-bit binary representation
2.- (207)10=(x)2
3.- (-135)10=(x)2 # In a two-complement representation
4.- (2D7)16=(x)2
5.- (-3.3125)10=(x)2 #IEEE 754 standard, 32 bit representation
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- A(n) _____ operation transforms a 0 bit value to 1 and a 1 bit value to 0.For 10 bits floating point representation using: seeeefffff, what is the bias for denormalized numbers? A. 7 B. 6 C. 4 D. 3 E. 2 What is the range of integers that can be represented using 8 bits 2's complement? A. -127 to 127 B. -128 to 127 C. -127 to 128 D. 0 to 255 E. 0 to 256a) Use the two’s complement binary representation to represent each of the following integers as 10-bit binary numbers. i) -13710 ii) 14510 iii) -15810 iv) 16710 v) -11510 b) If an 8-bit binary number is used to represent an analog value in the range from 0 to 100kg, what does the binary value 011001002 represent?
- 1) Assume we have 8 bit (1 byte) 2's complement system with a 3-bit fractional. Find a decimal representation of 2's complements binary number 1011 0101.001 2) Assume we have a byte system for the fixed number representation (the whole number is presented with 8-bits (one byte) and the fractional part is presented with 2-bits), find the 2's complement of 0110 0010.01What will be the results of adding the following integers together assuming a 16-bit unsigned representation: 25534 and 40002 10000 and 55535 44456 and 27845 Clearly indicate the cases where the results overflow. What will be the results of adding the following integers together assuming all integers are represented as 16-bit 2's complement representation: 20000 and 12768 -20000 and -12768 12345 and 23456 Clearly indicate the cases where the results overflow.Binary Arithmetic Coding: Consider integer implementation of binary arithmetic coding: Use 4 bit integers to store LOW and HIGH. At certain stage, suppose the counters for 0 and 1 are 30 and 10 respectively LOW =2, HIGH = 13, and E3 scaling counter Scale3 = 2; Describe the detains of the encoding process when the next two inputs bits are both 1;
- Convert the following decimal numbers to binary 4-bit two’s complementrepresentations, or explain why the conversion is not possible.a. 3 b. -5 c. -10Perform the following operation for the binary equivalent of the decimal numbers (-14) 10+ (-15) 10 The solution in 8 bit representation ?IEEE 754-2008 contains a half precision that is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. Write down the bit pattern to represent -1.625 * 10-2 assuming a version of this format. Calculate the sum of 2.625*102 and 4.150390625 * 10-1 by hand, assuming both numbers are stored in the 16-bit half precision described above. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps.
- IEEE 754-2008 contains a half precision that is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. Write down the bit pattern to represent -1.5625 * 10-2 assuming a version of this format. Calculate the sum of 2.6125*102 and 4.150390625 * 10-1 by hand,assuming both numbers are stored in the 16-bit half precision described above. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps.Find the following differences for a signed binary representation a 111000 -110011 (signed 6-bit representation) b. 11001100 -101110 (signed 8-bit representation) c. 111100001111 -110011110011 (signed 12-bit representation) d. 11000011 -11101000 (signed 8-bit representation)True/False The number of distinct values represented in a 32-bit sign-magnitude binary representation is identical to the number of numbers represented in a 32 bit 2's complement notation.