![]() We are urged to be filled with the Spirit as well (Ephesians 5:18 Galatians 5:16, 25). The Bible records many mighty things done when people were filled with (i.e., controlled by) the Holy Spirit (Exodus 31:2–3 Ezekiel 43:5 Luke 1:67 Acts 4:31). We can bear everlasting fruit for God’s kingdom, and we can overcome impossible challenges when the Holy Spirit fills our hearts until our “cup runneth over.” In Christ we can have overflowing joy, overflowing love, and overflowing peace. He is not stingy, nor are His blessings confined to temporal things. ![]() Paul continues that theme in Ephesians 3:20 and describes God as the One “who is able to do immeasurably more than all we ask or imagine.” Romans 8:37 promises that we are “more than conquerors through Him who loves us.” The message echoed in each passage is that of God’s excessive grace and provision for every area of our lives. Jesus reflected God’s generosity when He said, “The thief comes only to steal and kill and destroy I came that they may have life, and have it abundantly” (John 10:10). The Bible emphasizes the excessive love, blessing, and power that God desires to pour out on those who love Him (Malachi 3:10 Lamentations 3:22 Psalm 108:4). This abundance is not limited to material blessings under the Old Covenant, but it also includes the Holy Spirit’s future outpouring upon all who ask (Luke 11:13 Acts 2:1–4). The Lord not only gives His people what they need (Psalm 23:1–2), but He supplies abundance in the midst of difficult times (verse 5). The emphasis of Psalm 23 is the Good Shepherd’s loving care for His sheep (cf. Other versions say “my cup overflows.” A cup runs over when it cannot hold all that is being poured into it. On the other hand, 2^1023 is well within the representable range for a 64-bit number and can therefore be displayed accurately.The phrase my cup runneth over is the King James Version’s wording of Psalm 23:5. In the case of 9007199254740993, which is larger than the largest number that can be represented using 64 bits, the computer cannot represent it exactly and therefore it is rounded to the nearest representable number. This means that the largest number that can be represented using 64 bits is 2^64 - 1, which is approximately 1.8 x 10^19. In most modern computers, numbers are represented using a fixed number of bits, typically 32 or 64 bits. Regarding your second question, the reason why a computer can display 2^1023 (8.98846567431158e+307) but not 9007199254740993 is due to the way that numbers are represented in the computer's memory. However, in practice, these approximations are usually accurate enough for most applications. This means that for numbers that require an infinite number of bits to represent exactly, such as irrational numbers like pi, the computer can only represent an approximation of the number. Modern computers use finite-precision arithmetic to perform computations, which means that they can only represent numbers with a limited number of bits. I cound not answer ur problem and look around for a bit and found this: I also recommend this explanation of floating point representation: Try clicking the 1s or 0s to see what happens when they take on different values. ![]() It currently represents 0.75 in 64-bit floating point. I find it helpful to see what happens when you change bits in a representation. If it goes above that, then the exponent can be increased instead. The key thing here is that the mantissa only ever needs to be between 1.0 and 2.0 (excluding 2). In this case, there is a 1 in the first bit, so this mantissa is 1.5. The goal is for those bits to be able to represent values between 0 and 1, which then is considered a mantissa between 1 and 2. According to the floating point standard, the first bit represents 1/2 (0.5), the second bit represents 1/4, the third bit represents 1/8, etc. 1022-1023 is -1, which is indeed the exponent. ![]() According to the floating point standard, the exponent is calculated by subtracting 1023 from that value. The next 11 bits represents the exponent -1: The first bit represents the sign, where 0 is positive. The floating point representation of 0.750 in binary needs to include the sign (positive/negative), the mantissa, and the exponent. The number -1 is called the "exponent" (as per normal math term). The number 1.5 is called either the "mantissa" or the "significand". Let's step through how the computer actually represents that number in floating point representation and see if that helps. From the author: Apologies for the confusing explanation.
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