1. Name the four ways in which signed integers can be represented in digital com
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Question
1. Name the four ways in which signed integers can be represented in digital computers, and explain the differences.
2. Which one of the four representations for signed integers is used most often by digital computer systems?
3. What is the minimum number of bits needed to count to 205?
4. How high can someone count with 5 bits?
5. Represent the following decimal numbers in binary using 8-bit signed magnitude, one’s complement, two’s complement, and excess-127 representations.
a. 77
d. -42
c. 119
d. -107
Explanation / Answer
Question 1. Name the four ways in which signed integers can be represented in digital computers, and explain the differences.
Answer 1:
Number Systems
Human beings use decimal (base 10) and duodecimal (base 12) number systems for counting and measurements (probably because we have 10 fingers and two big toes). Computers use binary(base 2) number system, as they are made from binary digital components (known as transistors) operating in two states - on and off. In computing, we also use hexadecimal (base 16) or octal(base 8) number systems, as a compact form for represent binary numbers.
Decimal (Base 10) Number System:
Decimal number system has ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, called digits. It uses positional notation. That is, the least-significant digit (right-most digit) is of the order of 10^0 (units or ones), the second right-most digit is of the order of 10^1 (tens), the third right-most digit is of the order of 10^2 (hundreds), and so on. For example,
We shall denote a decimal number with an optional suffix D if ambiguity arises.
Binary (Base 2) Number System:
Binary number system has two symbols: 0 and 1, called bits. It is also a positional notation, for example,
We shall denote a binary number with a suffix B. Some programming languages denote binary numbers with prefix 0b (e.g., 0b1001000), or prefix b with the bits quoted (e.g., b'10001111').
A binary digit is called a bit. Eight bits is called a byte (why 8-bit unit? Probably because 8=23).
Hexadecimal (Base 16) Number System:
Hexadecimal number system uses 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, called hex digits. It is a positional notation, for example,
We shall denote a hexadecimal number (in short, hex) with a suffix H. Some programming languages denote hex numbers with prefix 0x (e.g., 0x1A3C5F), or prefix x with hex digit quoted (e.g.,x'C3A4D98B').
Each hexadecimal digit is also called a hex digit. Most programming languages accept lowercase 'a' to 'f' as well as uppercase 'A' to 'F'.
Octal (Base 8) Number System:
Octal and hex are convenient ways to represent binary numbers, as used by computers. Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" or "hex", number format. In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers. In an octal system, there are only 8 digits, 0 through 7.
Question 2. Which one of the four representations for signed integers is used most often by digital computer systems?
Answer 2:
The sistem binary (base 2) it is the most currently used by digital systems.
Question 3. What is the minimum number of bits needed to count to 205?
Answer 3:
for 205 is 8bits -> 11001101
Question 4. How high can someone count with 5 bits?
Answer 4:
Question 5. Represent the following decimal numbers in binary using 8-bit signed magnitude, one’s complement, two’s complement, and excess-127 representations.
a. 77
d. -42
c. 119
d. -107
Answer 5:
a. 77 -> binary 1001101
b. -42 -> binary -101010
c. 119 -> binary 1110111
d. -107 -> binary 1101011
Count cyfer Max count-Dec Max count- Binary 5 100.000 32Related Questions
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