2x -1
What is the decimal equivalent of the largest binary integer that can be obtained with (a) 11 bits and (b) 25 bits?
To get the 2s complement, change all 1 bits to 0s and all 0 bits to 1s, and add 1 to the result. So the 2s complement of the 8-bit binary number 10001011 is the binary integer 01110101. If you want that in decimal, then remember that each place value column is twice the value of the place value column to its right, and the rightmost place value column for an integer is 1. Thus 01110101 in decimal is 64 + 32 + 16 + 4 + 1 = 117 (And 10001011 as a signed 8-bit binary integer represents the decimal integer -117.)
Binary bits are necessary to represent 748 different numbers in the sense that binary bits are represented in digital wave form. Binary bits also have an exponent of one.
32
255
2x-1
What is the decimal equivalent of the largest binary integer that can be obtained with (a) 11 bits and (b) 25 bits?
65,535 in decimal = 1111111111111111 in binary.
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The largest integer is 211 - 1 which is 2048 - 1 = 2047
The highest unsigned integer is 255; The highest signed integer is 127.
The true answer is yes and no Yes: in binary coded decimal and hexadecimal each byte is 4 bits long; in octal each byte is three bits long. No: in true binary theoretically there is no "last bit".
To get the 2s complement, change all 1 bits to 0s and all 0 bits to 1s, and add 1 to the result. So the 2s complement of the 8-bit binary number 10001011 is the binary integer 01110101. If you want that in decimal, then remember that each place value column is twice the value of the place value column to its right, and the rightmost place value column for an integer is 1. Thus 01110101 in decimal is 64 + 32 + 16 + 4 + 1 = 117 (And 10001011 as a signed 8-bit binary integer represents the decimal integer -117.)
An 8-bit unsigned integer can represent values ranging from 0 to 255. This is because, with 8 bits, there are (2^8 = 256) possible combinations of binary digits. Therefore, the smallest value is 0 (all bits are 0) and the largest value is 255 (all bits are 1).
Converting Gray Code to Binary1). Write down the number in gray code.2). The most significant bit of the binary number is the most significant bitof the gray code.3). Add (using modulo 2) the next significant bit of the binary number to thenext significant bit of the gray coded number to obtain the next binary bit.4). Repeat step 3 till all bits of the gray coded number have been added inmodulo 2. The resultant number is the binary equivalent of the gray number.Converting Binary to Gray Code1). Write down the number in binary code.2). The most significant bit of the gray number is the most significant bitof the binary code.3). Add (using modulo 2) the next significant bit of the binary number to thenext significant bit of the binary number to obtain the next gray coded bit.4). Repeat step 3 till all bits of the binary coded number have been added inmodulo 2. The resultant number is the gray coded equivalent of the binarynumber.
Binary bits are necessary to represent 748 different numbers in the sense that binary bits are represented in digital wave form. Binary bits also have an exponent of one.
BCD is used for binary output on devices that only display decimal numbers.