[8.1] Calculate the sum of 2.6125 x 10¹ and 4.150390625 × 10¹ by hand, assuming A and B are stored in the 16-bit half precision. Assume 1 guard, 1 round bit, and I sticky bit, and round to the nearest even. Show all the steps.

Assume that a mad scientist has created a computer that has 12-bit registers (storage). The most significant bit is the sign bit. He wants to execute the following computation using 12-bit register. 124-435 (Subtract decimal 435 from decimal 124) Use 2's complement method (in binary) to find the result of the above operation in binary system. Then convert the result back to decimal to check your answer. NOTE: Please don't do the subtraction in decimal! Show all the computations in the answer. Paragraph В I +v Add a File Record Audio

5. Let the content of register $t1 represent a 2's complement number N. Write a MIPS code fragment such that the register $t2 stores the absolute value of N. In other words, register $t2 has a copy of register $t1 if N is positive, and $t2 should hold the negative of N, if N is negative.

1-4) For each of the following, assume the machine used is a 5 bit machine. Complete the table by identifying (a) how the decimal value on the left would be stored in 5 bits using a 2s complement representation, and (b) what the equivalent decimal value is for the bit pattern in part (a). number -17 +28 -54 +96 (a) 2's Complement (b) Decimal Equivalent 5) What is the resulting bit pattern when the unsigned 10 bit binary value 1001101101 is stored in an 8 bit container? Name: 6) What is the resulting bit pattern when the signed 10 bit binary value 1110101011 is stored in an 8 bit container? 7) What is the resulting bit pattern when the unsigned 8 bit binary value 1101001 is stored in a 10 bit container?

1.8 Show each of the following calculations in 4-bit two's complement notation. In each case, convert the result (in binary) back to a decimal number. (a) -5 + 7 (b) - 3 + 3 (c) 6 - 4 (d) -2 - 3

Construct a truth table in standard binary form for a function of four variables,F(W,X,Y,Z) = ABC,where ABC is the signed 3-bit sum of the signed 2-bit numbers WX and YZ.

[10] Write the 8-bit representation of –6810.

explain and provide a full solution.

Question 1. and {C,D} form the two 2-bit numbers N1 and N2. The circuit will perform the difference N1 – N2 and gives output bits F (MSB) and G. Assume that the circuit never sees the combinations of inputs in which N1 is less than N2 i.e. you can regard those input combinations as don't care Consider a 2-bit binary subtractor defined as follows. The inputs {A,B} conditions. а. Fill in the truth table for F and G. b. Fill in the K-map for the minimum sum of products expressions for the function F and G.

(3) The IEEE 754 standard specifies a single-precision binary floating-point format (binary32) as having 1 bit for sign bit, 8 bits for exponent, and 23 bits for fractions (mantissa). Given the conversion formula as follows, value2 = (-1)'31 × (1. b22b21 . bo)2 × 2(b30b29 .b23)2-127 ... (a) encode -2.2510 ; (b) decode 0 1000 0001 011 0000 0000 0000 0000 00002