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- The following is a quantity represented in base-8 (octal). What is its representation in base-10 (decimal)? (The right-most digit is still the one's place, the next is the 8s place, ...) 772Hexadecimal numbers are made using the sixteen digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.a. How many hexadecimal numbers are 4 digits long?b. How many 4-digit long hexadecimal numbers begin with A or B?c. How many hexadecimal numbers are 4 digits long with no repeating digits?d. How many hexadecimal numbers are 4 digits long and end in 6, and where the first digit must be from3 to 5? Digits can repeat.The sum of two binary numbers is 100000 and their difference is 1100. What are the binary numbers in decimal form? what is your answer for the first and second decimal number?
- A)The decimal number 162 what is the binary representation of it ? B)the decimal number of -53 what is the binary representation of it ?The Famous Gauss You must know about Gauss, the famous mathematician. Back in late 1700’s, he was at elementary school. Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher. He amazed his teacher with how quickly he found the sum of the integers from 1 to 100 to be 5050. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series, the second and second-last number in the series, and so on. For example:(1 + 100), (2 + 99), (3 + 98), ..., (50 + 51). Each pair has a sum of 101 and there are 50 pairs. History repeats itself. Jojo’s teacher assign a “busy work” to the students. The teacher believes that there will be no shortcut to finish this task in a minute. The teacher gives N integers A1, A2, ..., AN to the students. The teacher also gives Q questions. Each question contains two integers L and R asking the sum of all Ai where L <= Ai <= R. As a good friend of Jojo, help Jojo…WHAT IS THE 5-digit HEXADECIMAL REPRESENTATION OF EACH OF THE FOLLOWING SIGNED DECIMAL INTEGERS? A. -24 B. -31 C. -1 D. +25 E. +35
- 5. The following mumbers were origimally written using a check digit. Identify which Numbers are having Valid Check digits and which are having errors? Number Check digit 547854324 a. b. 107821687 c 458963123 3.1. Fill in the blanks (1) For the decimal number 36, its binary number is 111, its hex number is 【2】, and its BCD number is 【3】. (2) If the binary number is 1010 0101, then its 1's complement is 【4), the 2's complement is 【5】. (3) The ASCII code for '5' is [61, the ASCII code for character 'B' is_【7】. (4) In microcomputer there are three types of buses, they are [81,data bus, and [191. (5) If CS=2500H, DS=3200H, SS=4300H, IP=2200H, SP-3000H, the physical address of the next instruction to be executed is 【10】 and the logical address of current stack top is 【1】 (6) For instruction MOV AX, [BX+6], the addressing modes of source operand is 【121, and the addressing modes of destination operand is 【13】. (7) For CPU 8088, when 16-bit data is pushed onto the stack, the stack pointer SP is [14], (increased by 2, decreased by 2) but when 16-bit data is popped off the stack, the stack pointer SP is 【15】 .(increased by 2, decreased by 2) (8) After the instructions MOV AX, 2500H and ADD AX, 2300H…A 36-bit floating-point binary number has eight bits plus sign for the exponent and 26 bits plus sign for the mantissa. The mantissa is a normalized fraction. Numbers in the mantissa and exponent are in signed-magnitude representation. What are the largest and smallest positive quantities that can be represented, excluding zero?
- 3. What decimal value does the 8-bit binary number 01101110 have if:a. It is interpreted as an unsigned numberb. It is on a computer using two’s complement representation PS: Please do them in a word processor and not hand-written!Perform the following subtractions. Assume that all numbers are in 2’scomplement notation. State the carry-in and carry-out, whether overflow or not,and if the result is correct. 11101101 – 00101010What decimal value does the 8-bit binary number 10101110 have if: a) it is interpreted as an unsigned number? b) it is on a computer using signed-magnitude representation? c) it is on a computer using one's complement representation? d) it is on a computer using two's complement representation? e) it is on a computer using excess-127 representation?