A 12-bit digital value can represent 4096 (212) different numbers. A 16-bit digital value can represent 65536 (216) different numbers. In the case of the LabJack U12, a single-ended analog input has a voltage range of -10 volts to +10 volts (20 volt total span) and returns a 12-bit value.

For example, a 16-digit decimal integer requires up to ceil(16*3.32) = 54 bits. You have to be careful with this though; for example, ceil(25*3.32) = 83 (since 25*3.32 = 83), but 25-digit integers require 84 bits. You need to specify the constant with more precision to get the correct result.

1 Answer. The number of bits required to represent an integer n is ⌊log2n⌋+1, so 552002 will require ⌊2002log255⌋+1 bits, which is 11,575 bits.

Orders of magnitude (data)

Well, you just have to calculate the range for each case and find the lowest power of 2 that is higher than that range. For instance, in i), 3 decimal digits -> 10^3 = 1000 possible numbers so you have to find the lowest power of 2 that is higher than 1000, which in this case is 2^10 = 1024 (10 bits).

Hence, a microprocessor with 12-bit memory addresses can directly access 4096 words (4 Kw) of word-addressable memory.

Apparent diffusion coefficient (ADC) is a measure of the magnitude of diffusion (of water molecules) within tissue, and is commonly clinically calculated using MRI with diffusion-weighted imaging (DWI) 1.

ADC Selection Criteria to Consider

1. Resolution refers to the number of output bits that the ADC can generate per conversion.
2. Speed has to do with the device’s sampling rate – in other words, what is the highest number of conversions per second that the ADC can handle?
3. Accuracy is relatively straightforward.

flash ADC

The resolution of the ADC is the number of bits it uses to digitize the input samples. For an n bit ADC the number of discrete digital levels that can be produced is 2n. Thus, a 12 bit digitizer can resolve 212 or 4096 levels.

Therefore, the 12-bit converter with 9.67 bit ENOB can only measure a signal to 0.1% accuracy. The dynamic range of the converter is approximately 60 dB, rather than 74 dB (ideal 12-bit ADC)….Converter Inaccuracies in a Signal Chain.

An ADC generates a digital output that’s proportional to the ratio of the input voltage to the input range. The resolution (Δ or least significant bit) is this range divided by the total number of possible steps. For example, an 8-bit ADC with a 2.048-V input range has a resolution of 8 mV (2.048 V/28 steps).

Another method for increasing the effective resolution of the ADC is oversampling and decimation. This technique involves oversampling of the input signal so that a number of samples can be used to compute a virtual result with greater accuracy than a single real sample can provide.

Sensitivity is an absolute quantity, the smallest absolute amount of change that can be detected by a measurement. Consider a measurement device that has a ±1.0 volt input range and ±4 counts of noise, if the A/D converter resolution is 212 the peak-to-peak sensitivity will be ±4 counts × (2 ÷ 4096) or ±1.9 mV p-p.

Requirements To Increase SNR That is, the dynamic range of the input signal must match the reference voltage of the ADC. If not, the SNR will be lower than that calculated using Equation 3. If the ADC used to measure a parameter is 12-bits and not oversampled, then the best SNR (calculated using Equation 3) is 74 dB.

The higher the resolution of the ADC for a given input signal range, the smaller the quantization error as the number of possible output codes for the given input signal range increases. This effect is sometimes referred to as a many-to-one mapping.