Think like a computer! Pure Binary! Quiz

Answer: 00000000, carry flag set

The carry flag is like a ninth bit for many operations. So with adding 10110110 and 1001010 resulting in 100000000, the eight zeroes are placed in the destination register, and ninth bit, 1, is placed in the carry flag, setting it. A flag is simply a bit which is set when 1 and clear when 0.

Answer: Doubling the value

The computer inserts a zero on the right after shifting all bits left. As we are working with binary values, adding a zero to the end of a binary number is equivalent to multiplying the binary number by binary 10 or two. A computer inserts a zero to the left and dumps the rightmost bit after a shift right, which is equivalent to halving the value (and rounding down).

Answer: 10110000, carry flag clear

A computer does not stop shifting when the carry flag is set. The program would have had to react to the setting of a flag. Since we just shifted left four times without stopping, we got interesting results. The first and second shifts were straight forward, to 01010110 and to 10101100, with 0 in the carry flag after both. On the next shift, the register contains 01011000, and the carry flag contains 1, and is set.

But because we did not stop and shifted once more, the last shift placed a 0 in the carry flag, clearing it. We lost that last bit. If our goal had been to multiply the value in the register by sixteen (four doublings), we failed, because we did not account for the limited size of the register.

Answer: Remainder bit

Since shifting bits to the right is equivalent to dividing the contents by binary 10 (or two), the bit that shifts into the carry bit ends up being the remainder of that division. The remainder after dividing by two is either one or zero.

Answer: 01000100

The bit-wise AND operation compares each bit position in one register to each bit position in the other register. That same position in the result is 1 only if the bit of one register AND the bit of the other register are both 1. In other words 1 AND 1 is 1, 1 AND 0 is 0, 0 AND 1 is 0, and 0 AND 0 is 0.

Answer: 01111111

The bit-wise OR operation compares each bit position in one register to each bit position in the other register. That same position in the result is 1 if either the bit of one register OR the bit of the other register is 1. In other words 1 OR 1 is 1, 1 OR 0 is 1, 0 OR 1 is 1, and 0 OR 0 is 0.

Answer: Inverting the bit values and adding one. Pos: 00010100, Neg: 11101100

The scheme picked for representing negative values is called "two's complement". The other examples, inverting all bits (called "one's complement") and simply setting the leftmost bit (sometimes called "signed magnitude"), can work to represent negative values but both schemes represent zero in two different ways, which complicates things.

Inverting bit values and subtracting one is not a feasible scheme for representing negative values. There is a better scheme where numbers are represented in order from lowest negative to highest positive.

It is called "excess" or "offset". It is the similar to two's complement except the leftmost bit is inverted where 1 represents a positive value and 0 represents a negative value. This scheme was not used because unsigned and equivalent positive signed values didn't match up. (They were offset.)

Answer: It represents the sign of the value

The leftmost bit is commonly referred to as the sign bit when representing integer values. The signed values represented in one-byte is -128 to -127. Only the right seven bits represent the magnitude, whereas with unsigned values where the leftmost bit does not represent the sign values can range from 0 to 255.

The value -128 is represented by 10000000. Reversing the two's complement to get the positive, subtract 1 (01111111) and invert bits gets you 1000000 again, which, if unsigned, would instead represent +128.

Answer: A negative value, when using two's complement to represent signed values

Adding 01011000 and 00110000 results in 10001000, which represents either a positive value (132) or a negative value (-120) when using two's complement. If you using two's complement to represent negative values, you have just added two positive values resulting in a negative value, which could mean a possible bug in your programming! There is a special flag called an overflow flag that detects when this occurs.

Answer: 8-bit

Old game consoles, like NES, used 8-bit processors. The earliest IBM PC used the Intel 8088 processor, a 16-bit processor with an 8-bit bus. (Memory was still accessed in 8-bit pieces.) Windows had to be upgraded not to long ago to work on 32-bit processors, the common processors of today. Now the common user is beginning to make the transition to 64-bit processors. Think of the progression: from 8-bit registers holding integer values ranging from -128 to +127 to 16-bit registers holding integer values ranging from -32,768 to +32,767 to 32-bit registers holding integer values ranging from −2,147,483,648 to +2,147,483,647 to 64-bit registers working with integers from -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807, a range so large software developers don't even bother looking up the range! And there are 128-bit processors out there....