In binary, each place's weight grows by a power of 2. That's why decimals are called a base ten system. In the above diagram, you can see that the growth of each place's weight is in the powers of 10, starting from 10^0 and going through 10^5. We multiply the digits in each place by their place's weight and sum them all up to get a complete number. The weight of the hundredth place is one hundred. These powers of 10 in each place are the weights of the places. We assign the one's place to the first digit from the right, then the ten's place to the second from the right, the hundredths to the third, and so on, growing each time by power of 10. Let's take a look at how our minds do this. If I tell you to read out 872500, you will likely say 872.5K. Let's first see how decimal numbers are represented in binary and how to add two binary values. Understanding the challenges and the beauty of binary arithmetic design (of positive and especially negative integers) is one of the most fundamental concepts in a computer processor. Ultimately computers are just a fast arithmetic machines with logic capabilities. This is because sophisticated operations like subtraction, multiplication, and division utilize adders in their circuits. The whole responsibility of making computers compute lay on the shoulders of adders – circuits that add two numbers. The design of early computers such as EDVAC started with the desire to make tedious mathematical calculations easier and faster. EDVAC was one of the earliest electronic binary computer built for the U.S. This means that the value of eax after executing ADD eax, 42 will be 20 + 42 = 62. The ADD eax, 42 assembly code is designed to add 42 to the current value of the eax register (accumulator) and stores that sum in eax. The eax register is called an accumulator in most processors. The decoded output says that the opcode is ADD and the operands are eax and 42.Įax is a register – a memory location inbuilt into the processor that can be accessed instantaneously by the processor. When the fetching of the machine code for ADD eax, 42 from the memory finishes, the instruction is decoded. Then it is stored into the main memory before the fetch-decode-execute cycle can begin. In the ALU, the instruction is executed based on the opcode on the operands and the result is stored back in the memory.įor example, the assembly code ADD eax, 42 is first turned into machine code (0s and 1s) by the assembler. The decoded instructions are sent to the Arithmetic and Logic Unit (ALU) for execution. The operands are the values (or memory locations) on which that operation will be performed. The opcode decides the further action that needs to be performed like ADD (addition), JMP (jump), INC (increment) and so on. The processor starts the execution cycle by fetching the instructions from the main memory, then the control unit of the processor decodes those instructions into two parts – operation code (opcode) and operands. Every digital computer follows this cycle to run machine code. The fetch decode execute cycle architected by Sir John von Neumann. Those set of 0s and 1s known as machine code (or machine instruction) are first stored in our computer's main memory (RAM) before the processor can execute them. The software programs we code get to 0s and 1s via compilers and assemblers. Software, images, text, videos, numbers and everything in between are 0s and 1s at the lowest level in our computer.įor images, text, videos and numbers, we have encoding schemes that decide how these stuff will get to 0s and 1s. First, some background on how computers work Let's explore the beauty of those techniques. Since computers can use only two digits – 0 and 1 – engineers and mathematicians back in the day designed clever techniques for representing negative numbers and for doing arithmetic with them. This system uses digits from 0 to 9 along with plus and minus signs (+ and -) to denote positive or negative numbers. We humans, on the other hand, communicate numbers via the decimal system. One of the first things we learn about computers is that they only understand 0s and 1s, or bits.
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