Base-2:
Base-2 number system consists of binary numbers “0” and “1”. The base-2 number system is a positional notation with a radix of 2.
Base-10 number system:
Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.
Base 10:
Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.
Base-8:
Base-0 number system uses the value 0 through 7. The base-8 number system is a positional notation with a radix of 8.
Base 10:
Decimal is the base-10 number system, which only uses the digits 0 through 9. The base-10 number system is a positional notation with a radix of 10.
Base-16:
The base 16 represents the hexadecimal number system. Hexadecimal number system consists of sixteen digits from 0 to 9, and from 10 to 15 is represented in the form of letters from A to F.
Explanation of Solution
Representing
To represent a positive decimal number in 16-bit excess notation, the binary equivalent of the number is added to
Binary equivalent of number 515 represented 16 bits:
Therefore,
Explanation of Solution
Representing
The two’s complement notation of any non-negative decimal number is the decimal equivalent of number. So, the binary equivalent of
Therefore, the two’s complement notation of
Representing
The two’s complement notation of negative decimal number is calculated by adding 1 to the complement of the binary equivalent of the number
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Chapter 3 Solutions
Systems Architecture
- A(n) __________ is an integer stored in double the normal number of bit positions.arrow_forwardConvert IEEE Single-Precision Binary Format Real number 11000100101001000010101000000000 to decimal. Please show all the steps. a) [1] What is the sign? b) [1] What is the biased exponent value? c) [1] What is the unbiased exponent value? d) [2] What is the normalized representation of the number in BINARY? e) [1] What is the unnormalized representation of the number in BINARY? f) [1] What is the decimal value of the whole number part of the number? g) [2] What is the decimal value of the fractional part of the number? h) [1] What is the real number in base 10arrow_forwardWhat decimal value does the 8-bit binary number 10011110 have if (Please show the calculation process): It is on a computer using one’s complement representation? 2.It is on a computer using two’s complement representation?arrow_forward
- With Fixed-length Binary Numbers: What is the decimal representation of the 10-bit signed binary number 01_0001_0001? What is the decimal representation of the 16-bit signed binary number 0000_0001_0001_0001?arrow_forwardwhat is 8 and 1 as a binary number?arrow_forwardWhat decimal value does the 8-bit binary number 10010110 have if it is represented using Excess-M representation?arrow_forward
- 1.What is the minimum number of binary bits needed to represent each of the following unsigned decimal integers? 4095 65534 42319 2.What is the hexadecimal representation of each of the following binary numbers? 0011 0101 1101 1010 1100 1110 1010 0011 1111 1110 1101 1011 3.What is the binary representation of the following hexadecimal numbers? 0126F9D4 6ACDFA95 F69BDC2A 4.What is the unsigned decimal representation of each of the following hexadecimal integers? 3A 1BF 1001 5.What is the unsigned decimal representation of each of the following hexadecimal integers? 62 4B3 29Farrow_forwardWhat is the largest & smallest binary number that can be expressed with 12 bits?arrow_forwardWHAT IS THE 5-digit HEXADECIMAL REPRESENTATION OF EACH OF THE FOLLOWING SIGNED DECIMAL INTEGERS? A. -24 B. -31 C. -1arrow_forward
- 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?arrow_forward3. 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!arrow_forwardHow can binary values be converted into unsigned and signed integers?arrow_forward
Systems ArchitectureComputer ScienceISBN:9781305080195Author:Stephen D. BurdPublisher:Cengage Learning