# Embedded systems: introduction to ARM® Cortex(TM)-M by Jonathan W Valvano

By Jonathan W Valvano

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Additional resources for Embedded systems: introduction to ARM® Cortex(TM)-M microcontrollers

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Observation: Bit 7 of an 8-bit number determines whether it is greater than or equal to 128. Number 100 100 36 4 4 4 0 0 Basis 128 64 32 16 8 4 2 1 Need it? 9. Example conversion from decimal to unsigned 8-bit binary to hexadecimal. 28: Give the representations of the decimal 45 in 8-bit binary and hexadecimal. 29: Give the representations of the decimal 200 in 8-bit binary and hexadecimal. One of the first schemes to represent signed numbers was called one’s complement. It was called one’s complement because to negate a number, we complement (logical not) each bit.

5. A hexadecimal number is a combination of its digits multiplied by powers of 16. To eliminate confusion between various formats, we will put a 0x or a \$ before the number to mean hexadecimal. Hexadecimal representation is a convenient mechanism for us humans to define binary information, because it is extremely simple for humans to convert back and forth between binary and hexadecimal. Hexadecimal number system is often abbreviated as “hex”. A nibble is defined as 4 binary bits, or one hexadecimal digit.

The basis of a number system is a subset from which linear combinations of the basis elements can be used to construct the entire set. The basis represents the “places” in a “place-value” system. For positive integers, the basis is the infinite set {1, 10, 100, …}, and the “values” can range from 0 to 9. Each positive integer has a unique set of values such that the dot-product of the value vector times the basis vector yields that number. For example, 2345 is the dot-product (…, 2,3,4,5) • (…, 1000,100,10,1), which is 2*1000+3*100+4*10+5.